Question

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

• A. $n.(n-1{)}^2..{.2}^2.1$
• B. $n.(n-1{)}^3..{.2}^3.1$
• C. $n.(n-1{)}^4..{.2}^4.1$
• D. $n.(n-1)...2.1$

Answer 1

Answer: (A)

$n.(n-1{)}^2..{.2}^2.1$

The way he can wear it in right hand $n!$ ways and left hand will be $(n-1)!$ ways
$=n!.(n-1)!$
$=n(n-1)!.(n-1)!$