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 selection be made?

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 the selection be made?

Solution:

6 people are to be selected from 8.

There are two case.

(i) When A is selected, then B must be chosen.

$\therefore$ Number of ways $={ }^{6} C_{4}=15$

(ii) When A is not chosen:

Number of ways $={ }^{7} C_{6}=7$

∴ Total number of ways = 15 + 7 = 22

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