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?

1 Answer
MathFact-orials.blogspot.com
Apr 5, 2017

#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#

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