Q. 233.7( 3 Votes )

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 :

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.


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