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 A $1920$

No of ways of choosing $1^{st}$ shoe$=10$

For $2^{nd}$ shoe$=8$ (It is not 9 because it contains the other pair of the $1^{st}$ chosen shoe)

and similarly, for $3^{rd}$ and $4^{th}$ are $6$ and $4$ respectively.

So, Total no. of ways$=10\times 8\times 6\times 4=1920$

ie, Option $A$ is correct answer.