Question

evaluate the following permutation: 9p4

Explanation:

Step1: Recall permutation formula

The formula for permutations is $_{n}P_{r}=\frac{n!}{(n - r)!}$. Here $n = 9$ and $r=4$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So $9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$ and $(9 - 4)!=5!=5\times4\times3\times2\times1$. Then $_{9}P_{4}=\frac{9!}{(9 - 4)!}=\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}$.

Step3: Simplify the expression

Cancel out the $5!$ terms in the numerator and denominator. We get $_{9}P_{4}=9\times8\times7\times6 = 3024$.

Answer:

3024