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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 12: Q6. (page 797)

Evaluate each expression.
$C (7, 2)$

Short Answer

Expert verified

21

Step by step solution

01

Step 1. Combination formula.

The number of combinations of $n$ objects taken $r$ at a time is the quotient of $n!$ and $(n - r)! r!$ , that is, $C (n, r) = \frac{n!}{(n - r)! r!}$ .

02

Step 2. Substitution.

Substitute 7 for $n$ and 2 for $r$ into combination formula.

$C (7, 2) = \frac{7!}{(7 - 2)! 2!}$

03

Step 3. Simplify.

Simplify the above obtained expression.

$\begin{array}{l} C (7, 2) = \frac{7!}{5! 2!} \\ = \frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \cdot 2 \cdot 1} \\ = 21 \end{array}$

The solution of given expression is 21.

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