A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a) If a study group is to consist of 2 freshmen, 3 sophomores, and 1 junior, 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?

Question

Mathematics

June

1 September, 19:46

A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a) If a study group is to consist of 2 freshmen, 3 sophomores, and 1 junior, 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?

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Answers (1)

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Keagan Cook · Answer 1

175/1001

Step-by-step explanation:

(a.)

Freshman: 5 Combination 2

sophomores: 7 Combination 3

Junior: 4 Combination 1

The combination of three groups:

=5c2 * 7c3 * 4c1

=10 * 35 * 4

=1400 ways

(b.)

=5+7+4=16

=2+3+1

Which is (16 combination 6)

The probability will be:

= (5c2 * 7c3 * 4c1) / 16c6

=1400/8008

=175/1001