Use a calculator to find the value below. $$ 21 \mathrm{P}_{5} $$ The calculator will display the answer

Question

UpStudy AI · Accepted Answer

We start with the permutation formula for $$ n \mathrm{P}_r $$:

$$
n \mathrm{P}_r = \frac{n!}{(n-r)!}
$$

For this problem, $$ n = 21 $$ and $$ r = 5 $$, so we have:

$$
21 \mathrm{P}_5 = \frac{21!}{(21-5)!} = \frac{21!}{16!}
$$

We can simplify the factorial expression by writing out the terms from 21 down to 17:

$$
\frac{21!}{16!} = 21 \times 20 \times 19 \times 18 \times 17
$$

Now, perform the multiplications step by step:

1. Calculate $$ 21 \times 20 $$:

$$
21 \times 20 = 420
$$

2. Multiply by 19:

$$
420 \times 19 = 7980
$$

3. Multiply by 18:

$$
7980 \times 18 = 143640
$$

4. Finally, multiply by 17:

$$
143640 \times 17 = 2441880
$$

Thus, the value displayed by the calculator is:

$$
2441880
$$
The calculator will display 2,441,880.

Use a calculator to find the value below. \( 21 \mathrm{P}_{5} \) The calculator will display the answer