Question

A history class is comprised of 4 female and 7 male students. If the instructor of the class randomly chooses 5 students from the class for an oral exam, what is the probability that 3 female students and 2 male students will be selected? Round your answer to 3 decimal places.

Answer 1

Solution: given that 4 female and 7 male students

P(3 female and 2 male student)

3 female students can be chosen in 4 ways because any individual one of the 4 girls can be left out. also because 4C3=4

2 students can chose from the 7 males in 7C2 = 21

so the number of ways that 3 girls and 2 boys can be chose in is 4*21 = 84

So the number of ways that any 5 students can be chosen from 15 students is 11C5 = 462

P(3 female and 2 male student) = 84/462 = 0.1818 = 0.182