Question

In: Statistics and Probability

A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a....

A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a. If a study group is to consist of 4 freshmen, 6 sophomores, and 2 juniors, how many different ways can the study group be selected? b. If a study group consisting of 6 students is selected, what is the probability that the group will consist of 2 freshmen, 3 sophomores, and 1 junior?

Solutions

Expert Solution

Solution:

Given:

A study group is to be selected from:

5 freshmen,

7 sophomores, and

4 juniors

Total = 16

Part a) how many different ways can the study group be selected if a study group is to consist of:

4 freshmen, 6 sophomores, and 2 juniors

4 freshmen from 5 freshmen can be selected in 5C4 ways

6 sophomores from 7 sophomores can be selected in 7C6 ways

and

2 juniors from 4 juniors can be selected in 4C2 ways

Thus

Total number of Ways = 5C4 X 7C6 X 4C2

Use following combination formula:

Thus

Total number of Ways = 5C4 X 7C6 X 4C2

Total number of Ways =5 X 7 X 6

Total number of Ways = 210

Part b) Find:

the probability that the group will consist of 2 freshmen, 3 sophomores, and 1 junior if a study group consisting of 6 students.

P( 2 freshmen, 3 sophomores, and 1 junior) =.........?

P( 2 freshmen, 3 sophomores, and 1 junior) = [ 5C2 X 7C3 X 4C1 ] / [ 16C6 ]

and

Thus

P( 2 freshmen, 3 sophomores, and 1 junior) = [ 5C2 X 7C3 X 4C1 ] / [ 16C6 ]

P( 2 freshmen, 3 sophomores, and 1 junior) = [ 10 X 35 X 4 ] / [ 8008 ]

P( 2 freshmen, 3 sophomores, and 1 junior) = 1400 / 8008

P( 2 freshmen, 3 sophomores, and 1 junior) = 0.174825

P( 2 freshmen, 3 sophomores, and 1 junior) = 0.1748


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