Permutations and Combinations — practice questions
122 curated practice questions from Permutations and Combinations (Mathematics JEE Main, NTA Exams) — 86 easy, 17 medium, 19 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.
- Number of ways in which 25 identical balls can be distributed among Ram, Shyam, Sunder and Ghanshyam such that at least…
- Coefficient of x^ 19 in the polynomial (x-1)(x-2) (x-20) is equal to :
- Three distinct numbers are selected numbers 1,2,3, , 15 , then probability that their sum is a perfect cube, is
- In how many ways can six boys and five girls stand in a row if all the girls are to stand together but the boys cannot…
- A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4…
- The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is
- From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a…
- There are 20 persons among whom two are brothers. Find the number of ways in which we can arrange them around a circle…
- The number of ways to give 16 different things to three persons A, B, C so that B gets 1 more than A and C gets 2 more…
- There are n points on a circle. The number of straight lines formed by joining them is equal to
- Let 15 toys be distributed among 3 children subject to the condition that any child can take any no. of toys. Find the…
- Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining these points are
- From a group of 10 men and and 5 women, four member committees are to be formed each of which must contain at least one…
- Ten different letters of a word are given. Words with five letters are formed from these given letters. Then, the…
- An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number…
- The total number of ways in which 11 identical apples can be distributed among 6 children is that at least one apple is…
- If n_ 1 r N and ^ n-1 C_ r = [k^ 2 -3 ] ^ n c_ r+1 then k lies in the interval
- In a touring cricket team, there are 16 players in all including 5 bowlers and 2 wicket-keepers. How many teams of 11…
- n letters are written to n different persons and address on the n envelopes are also written. If the letters are placed…
- Three branches of a bank in a city are managed by 4, 5 and 8 officers respectively. In how many ways 20 officers be…
- A man has 7 relatives, 4 of them are ladies and 3 gentlemen, his wife has 7 relatives and 3 of them are ladies and 4…
- Find the number of ways in which 5 boys and 5 girls can be seated in a row so that no two girls sit together.
- Number of rectangles in figure shown which are not squares is : array |l|l|l|l|l|l| & & & & & & & & & & & & & & & & & &…
- At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10…
- In how many ways the sum of upper faces of four distinct dice can be six ?
- A new flag is to be designed with six vertical strips using some or all of the colours yellow, green, blue and red…
- The total number of ways of arranging the letters AAAA BBB CC D E F in a row such that letters C are separated from one…
- In how many ways can 12 books be equally distributed among 3 students ?
- The total number of different combinations of one or more letters which can be made from the letters of the word…
- There are p points in a plane, no three of which are in the same straight line with the exception of q points which are…
- The set S = 1, 2, 3,..., 12 is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B…
- If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is
- The letters of word “Radhika” are permuted and arranged in alphabetical order as in English dictionary. The number of…
- Every one of the 5 available lamps can be switched on to illuminate certain Hall. The total number of ways in which the…
- 8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits…
- Number of ways in which 4 boys and 2 girls (all are of different heights) can be arranged in a line so that boys as…
- How many 9-letter words can be formed by using the letters of the word ALLAHABAD?
- The number of permutations of n different things, taken r at a time, in which P(r n-P) particular things will never…
- A library has ‘a’ copies of one book, ‘b’ copies of each of two books, ‘c’ copies of each of three books, and single…
- 4 buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by…
- How many 6 digit numbers that are divisible by 4 can be formed using the digits 0, 1, 2, 3, 4, 5 ?
- The number of ways to put 6 letters in 6 addressed envelopes so that all are placed in wrong envelopes, are
- Three couples (husband and wife) decide to form a committee of three members. The number of different committee that…
- The number of even numbers that can be formed by using the digits 1, 2, 3, 4 and 5 taken all at a time (without…
- How many words can be formed using letters of the word EQUATION so that it begins with E and ends with N?
- The number of straight lines that can be formed by joining 20 points no three of which are in the same straight line…
- The number of ways in which 52 cards can be divided into 4 sets, three of them having 17 cards each and the fourth one…
- The value of the expression 47 c_ 4 + _ j=1 ^ 5 52-j c_ 3 is equal to
- The number of all four digits numbers with distinct digits is
- Consider three boxes, each containing, 10 balls labelled 1, 2, ..., 10. Suppose one ball is randomly drawn from each of…
- How many words can be made by using letters of the word COMBINE which begins and ends with vowel ?
- If ^ n P _ 4 =24 ^ n C _ 5 , then the value of n is
- The greatest possible number of points of intersection of 6 straight lines and 4 circles is :
- A rack has 5 different pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be…
- Let T n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T n + 1 –…
- If a,b,c,d are odd natural numbers such that a + b + c + d = 20, then the number of values of (a, b, c, d) is :
- Find the number of numbers between 300 and 3000 that can be formed with the digits 0, 1, 2, 3, 4 and 5 (no digits being…
- In an election three districts are to be canvassed by 2, 3 and 5 men respectively. If 10 men volunteer, the number of…
- The total number of ways in which n 2 number of identical balls can be put in n numbered boxed (1, 2, 3, ......... n)…
- If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary…
- Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT - 1…
- There are five different green dyes, four different blue dyes and three different red dyes. The total number of…
- The interior angles of a regular polygon measure 150° each. The number of diagonals of the polygon is
- The number of six digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 & 7 so that digits do not repeat…
- The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 is equal to (if…
- The number of 3 digit odd numbers, that can be formed by using the digits 1, 2, 3, 4, 5, 6 when the repetition is…
- Given 6 different toys of red colour, 5 different toys of blue colour and 4 different toys of green colour. Combination…
- The letters of the word RANDOM are written in all possible orders and these words are written out as in a dictionary…
- How many six-digit, even numbers can be formed using the digits 0, 1, 2, 3, 4, 5 ?
- If all the words (with or without meaning) having five letters, formed using the letters of the words 'SMALL' and…
- A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 (without repetition). The total…
- There are p-points in a plane, no three of which are in the same straight line with the exception of q points, which…
- In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of…
- Five letters are put in 5 addressed envelops randomly, number of ways in which at least two letters go to the correct…
- There are 4 letter boxes in a post office. In how many ways can a man post 8 distinct letters ?
- The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three…
- If r, s, t are prime numbers and p, q are two positive integers such that LCM of p, q is r^ 2 5^ 4 t^ 2 , then the…
- Assuming the balls to be identical except for different in colors, the number of ways in which one or more balls can be…
- In how many ways a pack of 52 cards can be divided in 4 sets such that three of them have 17 cards each and fourth just…
- In an examination there are three multiple choice questions and each question has 4 choices out of which only one is…
- Total numbers of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is
- How many numbers lying between 500 and 600 can be formed with the help of the digits 1, 2, 3, 4, 5, 6 when the digits…
- How many words can be formed using the letters of the word EQUATION in which vowels occupy the 1 st , 3 rd , 4 th , 6…
- All possible three digits even numbers which can be formed with the condition that if 5 is one of the digit, then 7 is…
- If ^ n C_ r denotes the number of n things taken r at a time, then the value of expression ^ n C_ r+1 + ^ n C_ r-1 +2^…
- If _ r=1 ^ 25 ^ 54 c_ r ^ 54-r c_ 25-r =k ( ^ 54 c_ 25 ) , then K is equal to:
- There are m men and two women participating in a chess tournament. Each participant plays two games with every other…
- A rubber cube C= (x, y, z) 0 x, y, z 1 is cut by a sharp knife along the plane x=y, y=z and z=x . If no piece is moved…
- If the number of five digit numbers with distinct digit and 2 at the 10 th place is 336k, then k is equal to :
- If n and r are two positive integers such that n ≥ r, then ^ n C_ r-1 + ^ n C_ r is equal to :
- The number of ways in which 12 balls can be divided between two friends, one receiving 8 and the other 4, is
- If all the letters of the word “QUEUE” are arranged in all possible manner as they are in a dictionary, then the rank…
- A question paper on mathematics consists of twelve questions divided into three parts. A, B and C, each containing four…
- There are 9 candidates for an examination out of which 3 are appearing in Mathematics and remaining 6 are appearing for…
- There are n distinct points on the circumference of a circle. The number of pentagons that can be formed with these…
- How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ?
- 5 Indian and 5 American couples meet at a party and shake hands. If no wife shakes hands with her own husband and no…
- Two women and some men participated in a chess tournament in which every participant played two games with each of the…
- In how many ways, out of 5 persons to be arranged around a circular table, two particular persons can sit next to each…
- The number of ways of dividing 20 persons into 10 couples, is
- There are four candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The…
- On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are 20…
- 4 five rupee coins, 3 two rupee coins and 2 one rupee coins are stacked together in a column at random. The probability…
- If ^ n-1 C_ 3 + ^ n-1 C_ 4 > ^ n C_ 3 . then n is just greater than the integer
- How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd…
- Given below are two statements. STATEMENT - 1: There are 4 addressed envelopes and 4 letters for each one of them. The…
- If ^ 12 P_ r = ^ 11 P_ G +6^ 11 P_ 5 , then f is equal to :
- In how many ways can two balls of the same colour be selected out of 4 distinct black and 3 distinct white balls
- In how many ways can 7 plus (+) signs and 5 minus (-) signs be arranged in a row so that no two minus (-) signs are…
- The number of all possible different arrangements of the word “BANANA” is
- A father with 8 children takes them 3 at a time to the Zoological gardens, as often as he can without taking the same 3…
- The number of ways four boys can be seated around a round-table on four chairs of different colors is :
- The total number of times the digit 3 will be written when listing the integers from 1 to 1000 is
- How many ways can a triangle be drawn using any 3 of the 10 points that lie on a circle?
- How many of the 900 three digit numbers have at least one even digit ?
- The total number of selections of atleast one fruit which can be made from 3 bananas, 4 apples and 2 oranges is
- In how many ways can 15 identical blankets be distributed among 6 beggars such that everyone gets at least one blanket…
- The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee…
- If the letters of the word ‘mother’ are written in all possible orders and these words are written out as in a…
- All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such…
- The number of all three digit numbers having no digit as 5 is
- Five digit numbers divisible by 3 are formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such…