Question

This year, there are eight freshmen, ten sophomores, seven juniors, and eight seniors are eligible to be on a committee.

In how many ways can a dance committee of 8 students be chosen?

1.    ways

In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.

1. ways

In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 senions.

1. ways

Determine the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. Write your answer in decimal form, rounded to the nearest thousandth.

1. Answer:

Determine the probability of selecting a committee consisting of 4 juniors and 4 senions. Write your answer in decimal form, rounded to the nearest thousandth.

1. Answer:

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Total number of students = 8 + 10 + 7 + 8 = 33

a) Number of ways to select a dance committee of 8 students = 33C8

= 33!/(8! x 25!)

= 13,884,156

b) Number of ways to select 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors = 8C2 x 10C2 x 7C2 x 8C2

= 28 x 45 x 21 x 28

= 740,880

c) Number of ways to select 4 juniors and 4 seniors = 7C4 x 8C4

= 35 x 70

= 2,450

d) P(2 freshmen, 2 sophomores, 2 juniors, and 2 seniors) = 740,880/13,884,156

= 0.05336

e) P(4 juniors and 4 seniors) = 2,450/13,884,156

= 0.00018