Question

A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is :

• A. 120
• B. 140
• C. 160
• D. 180

Answer 1

The correct option is A 120

We have,

A box contains pair of shoes $=5$

Selected pair of shoes $=4$

Then,

Exactly one pair of shoes obtained is

${=}^5{P}_4$

$=\frac{5!}{(5-4)!}$

$=\frac{5!}{1!}=5!$

$=5\times 4\times 3\times 2\times 1$

$=120$

Hence, this is the answer.