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Question

A COMMITTEE OF 5 PEOPLE IS TO BE FORMED FROM 15 PARENTS AND 10 teachers. Find the probability that the committee will consist of at least one parent.

Answer 1

If there are n items, and want to choose k of them, then number of combinations are nC_k = n! / (n-k)! k!.
From the 10 teachers, pick a committee of 5 members → 10C₅

= 10! / (10 - 5)! 5! =

10! / 5! 5!

= 252 ways.
The total ways could make a committee from any of the 25(15 + 10) people → 10C₅

= 25! / (25 - 5)! 5!

= 25! / 20! 5!

= 53,130 ways.

Probability of no parent (P_{no parent}) = 10C₅/25C₅

= 252/53130

= 6/1265.

Probability of at least one parent = 1 - P_{no parent}.
= 1 - 6/1265
= 1 - 0.004743

= 0.9952.

The probability that the committee will consist of at least one parent is 0.9952.