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Monique wants to check out as many books by her favorite author as possible. She can check out 3 books at a time from her library, where there are 6 books available written by her favorite author.
How many different sets of 3 of these books can Monique choose?

Monique wants to check out as many books by her favorite author as possible. She can check out $3$ books at a time from her library, where there are $6$ books available written by her favorite author. $\newline$ How many different sets of $3$ of these books can Monique choose?

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Counting principle

Full solution

Q. Monique wants to check out as many books by her favorite author as possible. She can check out

3

books at a time from her library, where there are

6

books available written by her favorite author.

\newline

How many different sets of

3

of these books can Monique choose?

Problem Understanding: Understand the problem and determine the formula to use. $\newline$ Monique wants to choose $3$ books out of $6$ . This is a combination problem because the order in which she picks the books does not matter. The formula for combinations is $C(n, k) = \frac{n!}{k!(n-k)!}$ , where $n$ is the total number of items to choose from, $k$ is the number of items to choose, and ＂ $!$ ＂ denotes factorial.
Applying Combination Formula: Apply the combination formula to the problem. $\newline$ Using the formula $C(n, k) = \frac{n!}{k!(n-k)!}$ , we substitute $n$ with $6$ (the total number of books) and $k$ with $3$ (the number of books Monique wants to check out). $\newline$ $C(6, 3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!3!}$ .
Calculating Factorials: Calculate the factorials and simplify the expression. $\newline$ $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$ , $\newline$ $3! = 3 \times 2 \times 1 = 6$ . $\newline$ Now, we simplify the expression: $\newline$ $C(6, 3) = \frac{720}{(6 \times 6)} = \frac{720}{36} = 20$ .
Solution Conclusion: Conclude the solution. $\newline$ Monique can choose $20$ different sets of $3$ books from the $6$ books available by her favorite author.

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