Thank you for reporting, we will resolve it shortly
Q.
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
Permutations and Combinations
Solution:
Select $4$ pairs in ${ }^{5} C_{4}=5$ ways.
Now select exactly one shoe from each of the pair selected in $\left({ }^{2} C_{1}\right)^{4}$ ways.
This will fulfill the condition.
$\Rightarrow$ required answer $=5 \times 16=80$