Question

evaluate the following permutation: 7p3

Explanation:

Step1: Recall permutation formula

The formula for permutations is $_{n}P_{r}=\frac{n!}{(n - r)!}$, where $n = 7$ and $r=3$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $7! = 7\times6\times5\times4\times3\times2\times1$ and $(7 - 3)!=4!=4\times3\times2\times1$. Then $_{7}P_{3}=\frac{7!}{4!}=\frac{7\times6\times5\times4!}{4!}$.

Step3: Simplify the expression

Cancel out the $4!$ terms. We get $_{7}P_{3}=7\times6\times5 = 210$.

Answer:

210