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?
Given that we need to select 6 persons out of 8 persons, it is also mentioned that person B must be selected in the case of selection of A.
We need to find the no. of ways of selecting 6 persons.
The possible cases for the selection of 6 persons are:
i. selecting person A and person B and 4 others(similar to selecting 4 persons out of remaining 6 persons).
ii. selecting 6 persons other than person A and person B
Let us assume the no. of ways of selection be N.
N = (Selecting 4 persons from remaining 6 persons) + (Selecting 6 persons leaving Person A and B)
N = (6C4) + (6C6)
We know that ,
And also n! = (n)(n – 1)......2.1
⇒
⇒
⇒
⇒ N = 15 + 1
⇒ N = 16
∴ The no. of ways of selecting 6 persons is 16.