Question

We wish to select 6 persons from 8, but if the person A is chosen ,then B mist be chosen.In how many ways can the selection be made?

Answer 1

22

Explanation:

Let's first see that, without the selection limitation, we'd be picking 6 people from a group of 8 with no attention paid to the order in which the picks are made. This is a combination question, the general formula is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

`C_(8,6)=(8!)/((6!)(2!))=(8xx7xx6!)/(6!xx2)=28`

And so that is our limit on the answer - any answer we find bigger than 28 can't possibly be right.

Now to the question.

Let's see that if A is chosen, then B must also be chosen. If A is not chosen, B can still be chosen. So let's figure this out in two parts - where A is chosen and where A is not chosen.

A not chosen

When A is not chosen, we're picking 6 people from a group of 7:

`C_(7,6)=(7!)/((6!)(1!))=(7xx6!)/(6!)=7`

A chosen

When A is chosen, B must be chosen too. Since we're calculating a scenario where we know A is chosen and that B will also be a part of the group, there are 6 people left who can be chosen into the 4 remaining spots:

`C_(6,4)=(6!)/((4!)(2!))=(6xx5xx4!)/(4!xx2)=15`

Putting it together

We can now add the two scenarios together:

`7+15=22`