kevincanspain wrote:One more method to add to your repertoire:
Without the restriction concerning married couples, the number of committees consisting of 3 people would just be 8C3 = 8(7)(6)/3! = 56.
However, some of these have to be discarded, for they consist of an entire couple and a third person. How many must be discarded?
Good question.
We want to subtract all selections consisting of an entire couple and a third person. How many of selections are there?
To answer this question, let's break the task into stages.
Stage 1: Select 1 of the 4 couples.
We'll place both people in this couple on the committee.
There are 4 couples, so this stage can be accomplished in
4 ways
Stage 2: Select the third person for the committee
There are now 6 people remaining, so this stage can be accomplished in
6 ways.
By the Fundamental Counting Principle (FCP) we can complete both stages (and thus create a 3-person committee) in
(4)(6) ways
In other words, we can create
24 committees that break the rule.
From here, when we take all
56 possible committees and subtract the
24 committees that break the rule, we get
32
Cheers,
Brent
