Question

HELP!!! Evaluate 8^P7​

Answer 1

The correct answer is B. 40,320

Explanation:

In mathematics, a permutation refers to all the possible ways of arranging objects or elements in a set, while still considering an order. For example, you can calculate all the possible ways 5 athletes can end in a race as one athlete cannot have both the first and third place. The expression ${8}$$P_{7}$ shows a permutation because the P indicates the expression refers to a permutation. Additionally, this can be solved by using the formula ${n}$$P_{r}$  =$\frac{n!}{(n-r)!}$. This means, in the expression presented n = 8 while r = 7. Also, the symbol (!) indicates the number should be multiplied using all whole numbers minor to the given number until you get to 1, which is known as factorial functions. The process is shown below:

${n}$$P_{r}$  =$\frac{n!}{(n-r)!}$

${8}$$P_{7}$ = $\frac{8!}{(8-7) !}$

${8}$$P_{7}$ = $\frac{8!}{1!}$

${8}$$P_{7}$ = $\frac{8 x 7 x 6 x 5 x 4 x 3 x 2 x 1}{1}$   or  8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 1

${8}$$P_{7}$ = 40320