For a set of distinct objects

MATHEMATICS · Subjective · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations

Problem

For a set of

n

distinct objects, a committee of

r

members can be formed in several ways. (i) Give a logical explanation to show that the number of ways of choosing

r

objects from

n

objects equals the number of ways of choosing

(n-r)

objects from the same

n

objects. (ii) Using the result of part (i), rewrite

{}^{22}C_{3}

as a combination whose lower index is greater than

11

, and then calculate its value.