Question

A rack has $5$ different pairs of shoes. The number of ways in which $4$ shoes can be chosen from it, so that there will be no complete pair is

• A. $1920$
• B. $200$
• C. $110$
• D. $80$

Answer 1

The correct option is D $80$

We need to select 4 different pair of shoes, so that we don't get a complete pair, that means we need to select 4 shoes from 5 choices.

$\Rightarrow {{}^{5}C}_4$

Now from selected pairs we can choose any one of the shoe of the pair

${{}^{5}C}_4({{}^{2}C}_1\times {{}^{2}C}_1\times {{}^{2}C}_1\times {{}^{2}C}_1)=5\times 16=80$

Hence, $\left(D\right)$