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-

• A. 80
• B. 160
• C. 200
• D. None

Answer 1

Answer: (A)

80

Answer 2

Sol. Explanation:

Select 4 pairs in ⁵C₄ = 5 ways. Now select exactly one shoe from each of the pair selected in (²C₁)⁴ ways.

This will fulfill the condition.

̃ required answer = 5 × 16 = 80