Question

A group consists of four juniors and five seniors. Four students are chosen to participate in a local scavenger hunt. What's the probability that the selected group will consist of all seniors?

Answer 1

`5/126~=.039~=4%`

Explanation:

To get four seniors from a group of five, we can use the Combinations formula, the general equation of which is:

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

`C_(5,4)=(5!)/((4!)(1!))=5`

The number of ways four people can be picked from a group of nine (all the juniors and seniors combined) is:

`C_(9,4)=(9!)/((4!)(5!))=(9xx8xx7xx6xx5!)/(5!xx4xx3xx2)=3xx7xx6=126`

This gives the probability of getting all seniors in the selected group is:

`5/126~=.039~=4%`