The number of ways in which five different books to be distributed among 3 persons so…

Mathematics · JEE Advanced · NTA ExamsPermutations and Combinations

The number of ways in which five different books to be distributed among 3 persons so that each person gets at least one book, is equal to the number of ways in which
  1. 5 persons are allotted 3 different residential flats so that each person is alloted at most one flat and no two persons are alloted the same flat.
  2. number of parallelograms (some of which may be overlapping) formed by one set of 6 parallel lines and other set of 5 parallel lines that goes in other direction.
  3. 5 different toys are to be distributed among 3 children, so that each child gets at least one toy.
  4. 3 mathematics professors are assigned five different lectures to be delivered, so that each professor gets at least one lecture.

Answer

(B) number of parallelograms (some of which may be overlapping) formed by one set of 6 parallel lines and other set of 5 parallel lines that goes in other direction., (C) 5 different toys are to be distributed among 3 children, so that each child gets at least one toy., (D) 3 mathematics professors are assigned five different lectures to be delivered, so that each professor gets at least one lecture.

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