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.