Q4. - Algebra 1

Question

Evaluate each expression.

$\mathit{P}\mathbf{(}\mathbf{7}\mathbf{,}\mathbf{5}\mathbf{)}$

Step-by-Step Solution

Answer

2520

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 7 for $n$ and 5 for $r$ into permutation formula.

$P(7,5)=\frac{7!}{(7-5)!}$

Step 3. Simplify.

Simplify the above obtained expression.

 $\begin{array}{l}P(7,5)=\frac{7!}{2!}\\ =\frac{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{2\cdot 1}\\ =2520\end{array}$ 

The solution of given expression is 2520.