Probability of draws

Question

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

Answer 1

There are ₇C₅ = 7! / [5!(7-5)!] = 7*6/2 = 21 ways to choose 5 students from a total of 7.  

 

There are ₄C₃ = 4! / [3!(4-3)!] = 4/1 = 4 ways to select 3 female students from 4 female students

 

There are ₃C₂ = 3! / [2!(3-2)!] = 3/1 = 3 ways to select 2 male students from 3 male students 

 

Any of the 4 ways to select 3 females can be combined with any of the 3 ways to select 2 males to give 4*3 = 12 ways to select 3 females and 2 males  

 

Since each of the 21 possible selections is equally likely, and 12 of them satisfy the condition of having 3 females and 2 males, the probability that 3 females and 2 males will be selected is 12/21 = 4/7 ~ 0.571