Question

Teresa and Julia are among 10 students who have applied for a trip to Washington, D.C. Two students from the group will be selected at random for the trip. What is the probability that Teresa and Julia will be the 2 students selected?

Answer 1

`1/45`

Explanation:

For this question, we're looking at the number of ways we can satisfy a certain condition (having Teresa and Julia be picked) over the number of ways a group of 2 students can be picked.

Since we don't care in what order people are picked, we're working with combinations, where the general formula is:

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

How many ways can 2 people be picked from a group of 10?

`C_(10,2)=(10!)/((2!)(10-2)!)=(10!)/((2!)(8!))=(10xx9xx8!)/(2xx8!)=45`

There's only one combination that allows Teresa and Julia to be picked.

Putting it together, we have `1/45`