9. A study group is to be selected from a group of 16 students. The group consists of 5 freshmen, 7 sophomores, and 4 juniors. a) In how many ways can a group of 6 students be selected from this gr...
9. A study group is to be selected from a group of 16 students. The group consists of 5 freshmen, 7 sophomores, and 4 juniors.
a) In how many ways can a group of 6 students be selected from this group?
b) If the study group is to consist of 2 freshmen, 3 sophomores, and 1 junior, how many different groups are possible?
c) What is the probability that a group of 6 students will consist of 2 freshmen, 3 sophomores and 1 junior?
Homework Answers
a)
total 16 students
6 can be selected in 16C6 = 8008 ways
b)
2 freshmen can be selected in 5C2 ways
3 sophomores can be selected in 7C3 ways
1 junior in 4C1 ways
Hence required combinations are 5C2 * 7C3 * 4C1 = 1400
c)
requried probability = 1400/8008 = 0.1748
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