Q6. - Algebra 1

Question

Evaluate each expression.

$\mathit{C}\mathbf{(}\mathbf{7}\mathbf{,}\mathbf{2}\mathbf{)}$

Step-by-Step Solution

Answer

21

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

Step 2. Substitution.

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

 $C(7,2)=\frac{7!}{(7-2)!2!}$

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.