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

Question

A committee is to be formed to investigate what activities teenagers have available in small communities.  The committee is to have 7 members, chosen randomly from interested community members.  There are 10 parents, 5 teenagers, and 4 adults 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?  Express your answer to the nearest tenth of one percent.

Reiny · Answer

number of possible committees without restrictions
= C(19,7) = 50388

number of committees with the specified 4 adults
= 1 x C(15, 3) , (we must still choose 3 of the remaining 15)= 455

prob of your event = 455/50388 = 35/3876
= .0090
= appr .9%