Question

A rack has $5$ difference 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 $80$

Select $4$ pairs out of $5$ which can be done in $5C_4$ ways.

Now for every selected pair, select any one shoe can be done in ${\left(2C_1\right)}^4$ ways.

So, total no. of ways $=5C_4\times {\left(2C_1\right)}^4=80$