Question

What's the probability of picking Alex, Joan, and Karl as the 3-member sub-committee from a committee of 15 people? How many ways can a 3-member sub-committee be picked?

Answer 1

`1/455~=0.0022=0.22%`

Explanation:

We're working with combinations - we don't care in what order people are picked. The general formula for combinations is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

If we have a population of 15 `(n=15)` and we pick 3 people at a time `(k=3)`, we have:

`C_(15,3)=(15!)/((3!)(12!))=(15xx14xx13xx12!)/(6xx12!)=455` ways to pick 3 people.

The combination of Alex, Joan, and Karl are a single combination (again, we don't care if Alex is picked first, or Joan, or Karl). And so the probability of picking these 3 people as the sub-committee members is:

`1/455~=0.0022=0.22%`