Using the Fundamental Counting Theorem, it is found that there are:
- 61 ways to choose a single class rep.
- 7904 ways to choose three reps, one from each of the three Colleges.
- 11526 ways to choose three reps, one from each of the three Colleges, so that exactly one is female.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For a single class rep, there are 19 + 16 + 26 = 61 students, hence there are 61 ways to choose a single class rep.
For three reps, one from each college, we have that:
[tex]n_1 = 19, n_2 = 16, n_3 = 26[/tex], hence:
[tex]N = 19 \times 16 \times 26 = 7904[/tex]
7904 ways to choose three reps, one from each of the three Colleges.
Considering one female, we have that:
[tex]N = 13 \times 16 \times 26 + 19 \times 5 \times 26 + 19 \times 16 \times 12 = 11526[/tex]
11526 ways to choose three reps, one from each of the three Colleges, so that exactly one is female.
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866
