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We wish to select 6 persons from 8, but ...

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 the selections be made?

A

20

B

21

C

22

D

30

Text Solution

Verified by Experts

The correct Answer is:
C
Total number of person = 8
Number of person to be selected = 6
It is given that, if A is chosen then, B must be chosen.
Therefore, following cases arise.
Case I When A is chosen, B must be chosen.
Number of ways `= ""^(8 -2)C_(6-2) = ""^(6)C_(4)`
Case II When A is not chosen.
`therefore" "` Number of ways `= ""^(8 -1)C_(6) = ""^(7)C_(6)`
Hence, required number of ways `= ""^(6)C_(4) + ""^(7)C_(6)`
`= 15 + 7 = 22`
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