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Question
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
Solution
Total number of persons = 8
Number of persons to be selected = 6
Condition is that if A is choosen, B must be choosen
Case I: When A is choosen, B must be choosen
Number of ways = 6C4 ......[∵ A and B are set to be choosen]
Case II: When A is not choosen, then B may be choosen
∴ Number of ways = 7C6
So, the total number of ways = 6C4 + 7C6 ......[∵ There are two cases]
= 6C2 + 7C1 ......[nCr = nCn–r]
= `(6.5)/(2.1) + 7`
= 15 + 7
= 22 ways
Hence, the required number of ways = 22.
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