Question

A class consists of 3 students from Ashville and 4 from Bewton. A committee of 5 students is

chosen at random the class.a. Find the number of committees that include 2 students from Ashville and 3 from Bewton

are chosen.

b. In fact 2 students, from Ashville and 3 from Bewton are chosen. In order to watch a video,

all 5 committee members sit in a row. In how many different orders can they sit if no two

students from Bewton sit next to each other.

Answer 1

a.

The first member of the committee may be anyone from 3 students from Ashville.

The second member may be chosen from two remained Ashville students.

So the total number of possibilities to choose 2 students from 3 in some order is 3*2 = 6.

As for the committee, it is no matter in which order we select them, the number of unorder pairs is 3.

The same for Bewton. We have 5*4*3 = 60 ordered triplets students selected from 5.

These triplets may be ordered in 3*2 fashion. So the total number of unordered triplets is 10.

For any selected Ashvilles we may choose any triplet of Bewtons, so the total number of possible committees is 10*3 = 30

b.

The first place can occupy anyone from 3 students from Bewton.

The second place can occupy anyone from 2 students from Ashville.

The third place can occupy anyone from the remaining 2 students from Bewton.

The last two places are occupied by the remaining students from Ashville and Bewton, respectively.

So the total number of different orders is 3*2*2 = 12