Question

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?

Answer 1

Answer:

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