<3 asked in Science & MathematicsMathematics · 9 years ago

# A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four?

How many committees are possible if the committee must consist of the following?

Update:

Second part,

(a) one person from each class

(b) any mixture of the classes

20475

(c) exactly two seniors

Relevance
• 9 years ago

a)

Since there are four classes and we need to select one person from each, and we also need a committee of four.... there is only 1 way of doing this if you assume the individuals themselves are irrelevant and that the only consideration is the class. (the pigeonhole principle)

if you treat each individual as unique, however, then we must still select one from each class. But this is done by the fundamental counting principle. We multiple the sizes of each group, since we can pick ten from one class, eight from another, so on... 10 * 8 * 5 * 5 = 2,000

b) Any mixture of the classes. We assume now that class is irrelevant, but the individuals are unique. There are 10+8+5+5 = 28 individuals total. We must choose 4 of them. 28C4 = 20,475, as you already answered.

c) Exactly two seniors. We are choosing from two groups now. From the seniors alone there are 10C2 = 45 ways to choose two seniors. From the remaining 18 people, we must choose 2 more. There are 18C2 = 153 ways to choose two non-seniors. By the fundamental counting principle, we multiply them for 153 * 45 = 6,885 ways.

• strout
Lv 4
4 years ago

ideally, A, one individual from each and every type yet actually, not one of the above, the committee would be all Seniors. in case you placed it into balloting, the ten Seniors will trick the 5 beginners and get majority.