Q7. - Algebra 1

Question

Evaluate each expression.

$\mathit{P}\mathbf{(}\mathbf{6}\mathbf{,}\mathbf{3}\mathbf{)}$

Step-by-Step Solution

Answer

120

Step 1. Permutation formula.

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

Step 2. Substitution.

Substitute 6 for $n$ and 3 for $r$ into permutation formula.

 $P(6,3)=\frac{6!}{(6-3)!}$

Step 3. Simplify.

Simplify the above obtained expression.

$\begin{array}{l}P(6,3)=\frac{6!}{3!}\\ =\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{3\cdot 2\cdot 1}\\ =120\end{array}$

The solution of given expression is 120.