Probability

A history class is comprised of 7 female and 8 male students. If the instructor of the class randomly chooses 8 students from the class for an oral exam, what is the probability that 6 female students and 2 male students will be selected?

 

7 female and 8 male students

 

P(6 female and 2 male student) 

 

6 female students can be chosen in 7 ways because any individual one of the 7 girls can be left out.  

also because  7C6=7

2 students can chose from the 8 males in   8C2 = 28

so the number of ways that 6 girls and 2 boys can be chosein is  7*28 = 196

 

So the number of ways that any 8 students can be chosen from 15 students is 15C8 = 6435

 

 

P(6 female and 2 male student) = 196/ 6435