The combinatorial coefficient n–1 C p denotes

Mathematics · JEE Advanced · NTA Exams — Permutations and Combinations

1. the number of ways in which n things of which p are alike and rest different can be arranged in a circle.
2. the number of ways in which p different things can be selected out of n different thing if a particular thing is always excluded.
3. number of ways in which n alike balls can be distributed in p different boxes so that no box remains empty and each box can hold any number of balls.
4. the number of ways in which (n – 2) white balls and p black balls can be arranged in a line if black balls are separated, balls are all alike except for the colour.

Answer

(B) the number of ways in which p different things can be selected out of n different thing if a particular thing is always excluded., (D) the number of ways in which (n – 2) white balls and p black balls can be arranged in a line if black balls are separated, balls are all alike except for the colour.

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