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Q5.

Expert-verified
Found in: Page 797

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# Evaluate each expression.$\mathbit{C}\mathbf{\left(}\mathbf{10}\mathbf{,}\mathbf{4}\mathbf{\right)}$

210

See the step by step solution

## Step 1. Combination formula.

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

## Step 2. Substitution.

Substitute 10 for $n$ and 4 for $r$ into combination formula.

$C\left(10,4\right)=\frac{10!}{\left(10-4\right)!4!}$

## Step 3. Simplify.

Simplify the above obtained expression.

$\begin{array}{l}C\left(6,3\right)=\frac{10!}{6!4!}\\ =\frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\cdot 4\cdot 3\cdot 2\cdot 1}\\ =210\end{array}$

The solution of given expression is 210.