Q5. - Algebra 1

Question

Evaluate each expression.

$\mathit{C}\mathbf{(}\mathbf{10}\mathbf{,}\mathbf{4}\mathbf{)}$

Step-by-Step Solution

Answer

210

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

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

Step 3. Simplify.

Simplify the above obtained expression.

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

The solution of given expression is 210.