What is the probability that both captains will be eighth graders?

Question

Mrs. Donovan is the coach of a middle school golf team that has 10 golfers. There are 4 sixth graders, 2 seventh graders, and 4 eighth graders on the team. Mrs. Donovan will randomly select two team captains.

What is the probability that both captains will be eighth graders?

Answer 1

Use combinations. nCr = n!/ [(n-r)!r!] [# of ways of selecting r objects from a group of n]

# of way of selecting both captains to be 8th graders = 4C2 = 4!/(4-2)!2! = 6

#of ways of selcting 2 captains from 10 students = 10C2 =10!/ (10-2)!2! = 45

Then take the quotient to obtain the probability : 6/45 = 2/15