The number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
<h3>What is the rule of product in combinatorics?</h3>
If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
For the considered case, we have:
- There are 3 wolves to be included in first group.
- There are 8 female wolves, and 1 male wolf.
- 1 male wolf is sure to be in the first group.
So 2 spaces are remaining and are to be filled by 2 of 8 wolves.
Assuming that all 8 of them are distinguishable, choosing 2 of them is done in ways.
The first process of choosing male wolf for first place is done in 1 way only.
And the second process of choosing 2 female wolves can be done in 28 ways(ordering doesn't matter),
and since first and second process have no necessary order, using product rule, we get;
Number of ways of forming first group of wolves = ways.
Thus, the number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
Learn more about product rule here:
brainly.com/question/2763785