Name: Navi

Who is asking: Student

Level: Secondary

Question:

A committee is to be formed to investigate what activites teenagers have available in small communities. the committee is to have 7 members, chosen randomly form interested community members. there are 10 parents, 5 teenagers, and 4 adult without children who have all expressed an interest in serving on the committee.

what is the probability that the adults without children are all on the committee?

Hi Navi,
The probability you want is the number of forming a committee with all 4 adults without children and 3 others, divided by the number of possible committees.

Total number of people is 10 + 5+ 4 = 19. The number of possible committees is the number of ways of selecting 7 things from 19 things, that is

C(19,7)= 19!/(7!*12!) = 50388.
To form a committee with all 4 adults without children and 3 others you need to choose 3 people from the 15 who are not adults without children. The number of ways of forming such a committee is the number of ways of selecting 3 things from 15 things. What is this?
What is the probability?

Andrei and Penny