Question

Ms. De Leon wants to produce different sets of test questions for her essay test. If she plans to do this by putting together 3 out of 5 questions she prepared, how many different sets of questions could she contruct?
A.10
B. 20
C. 60
D. 80​

Answer 1

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C. 60

Answer 2

We need to recall the following definition of combination.

A combination is a way of selecting items from a collection, such that the order of selection does not matter.

Formula: $C(n,r)=\frac{n!}{r!(n-r)!}$

This problem is about the combination.

Given:

Ms. De Leon wants to produce different sets of test questions by putting together $3$ out of $5$ questions she prepared.

There are total $5$ questions and we are choosing $3$ questions.

Using the combination formula, we get

$C(5,3)=\frac{5!}{3!(5-3)!}$

$C(5,3)=\frac{5!}{3!2!}$

$C(5,3)=\frac{5\times 4\times 3\times 2\times 1}{(1\times 2\times 3)(1\times 2)}$

$C(5,3)=\frac{5\times 4}{2}$

$C(5,3)=10$

Thus, there are $10$ different sets of questions Ms. De Leon can construct.

Hence, the correct option is A. $10$.