Question

A closet has 5 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

Answer 1

5 pairs and we do not want respective left right shoes together

breaking up question
5 pairs de arrangement
4 to be chosen
D4= 24/2 + 24/6 + 24/24
= 12+ 4 +1
=17

choosing 4 out of 5 pairs
5C4

since above 2 methods are ways to complete one task
by principle of multiplication
5C4*17
=5*17
=85 ways