Question

At a high school the student government is made up of 5 seniors, 4 juniors, 3 sophomores and 2 freshmen. If there are 8 seniors, 9 juniors, 12 sophomores and 7 freshmen running, in how many ways can the student government be selected?

Answer 1

• 32598720

Explanation:

Combination for the school government requires:

• 5 out of 8 seniors = 8! / 3!5! = 6*7*8/2*3 = 7*8 = 56
• 4 out of 9 juniors = 9! / 4!5! = 6*7*8*9/2*3*4= 7*2*9 = 126
• 3 out of 12 sophomores = 12! / 3!9! = 10*11*12/2*3 = 10*11*2 = 220
• 2 out of 7 fishermen = 7! / 2!5! = 6*7/2 = 21

So number of total ways is:

• 56*126*220*21 = 32598720