Question

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

Answer 1

We select 4 pairs out of 5 which can be chosen through ${}^5{C}_4$ ways.

For every selected pair select any one shoe which can be done in (${}^2{C}_1{)}^4$ ways.

$\therefore$ Total no: of ways = ${}^5{C}_4\ast {(}^2{C}_1{)}^4$=80 ways.