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 ?

Answer 1

Total persons = 8

Selection to be made = 6 person If 4 is chosen then B must be chosen

$\Rightarrow$ A and B are chosen together

$\therefore$ Selection can be made in

${}^6{C}_4=\frac{6!}{4!2!}=\frac{6\times 5}{2}=15$ ways

Also the number of selections in which A and B are not chosen are ${}^7{C}_6=\frac{7!}{6!1!}$

= 7 ways

Total number of ways in which selection is made = 15 + 7 = 22 ways