Class 11

Math

Algebra

Permutations and Combinations

Given $n$ pairs of gloves, the number of ways can each of $n$ persons take a right handed and a left handed glove without taking a pair is

- $n.(n−1)_{2}...2_{2}.1$
- $n.(n−1)_{3}...2_{3}.1$
- $n.(n−1)_{4}...2_{4}.1$
- $n.(n−1)...2.1$

$=n!.(n−1)!$

$=n(n−1)!.(n−1)!$