In how many ways can 4 persons, out of 5 couples, be selected, such that there should be no pair (couple)?
Explanation:
We need to select 4 people out of 5 couples such that no couple is selected i.e., at max only one person will be selected from a couple.
First, we select 4 couples and then we will pick one from each of these 4 couples.
Number of ways of selecting 4 couples = 5C4 = 5 ways.
From each of these 4 couples either the female or the male could be selected i.e., 2 ways of selection.
∴ Total number of ways of selecting 4 people = 5 × (2)4 = 80.
Hence, option (c).
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