Question

evaluate the following permutation: $_{7}p_{4}$

Explanation:

Step1: Recall permutation formula

The formula for permutations is $_{n}P_{r}=\frac{n!}{(n - r)!}$. Here $n = 7$ and $r=4$.

Step2: Calculate factorial values

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

Step3: Simplify the expression

Cancel out the $3!$ terms in the numerator and denominator. We get $7\times6\times5\times4 = 840$.

Answer:

840