Question

What is 7P4



A: 28

B: 35

C: 210

D: 840

Answer 1

Answer:

D

Step-by-step explanation:

using the definition of n$P_{r}$ = $\frac{n!}{(n-r)!}$

where n! = n(n- 1)(n - 2)......× 3 × 2 × 1

here n = 7 and r = 4, hence

7$P_{4}$

= $\frac{7!}{3!}$

= $\frac{7(6)(5)(4)(3)(2)(1)}{3(2)(1)}$ ← cancel 3 × 2 × 1 leaving

7$P_{4}$ = 7 × 6 × 5 × 4 = 840 → D

Answer 2

The expression is an illustration of permutation.

The result of  $\mathbf{^7P_4}$ is (d) 840

The expression is given as:

$\mathbf{^7P_4}$

The formula of permutation is:

$\mathbf{^nP_r = \frac{n!}{(n-r)!}}$

So, we have:

$\mathbf{^7P_4 = \frac{7!}{(7-4)!}}$

$\mathbf{^7P_4 = \frac{7!}{3!}}$

Expand

$\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}$

$\mathbf{^7P_4 = 7 \times 6 \times 5 \times 4 }$

$\mathbf{^7P_4 = 840}$

Hence, the result of  $\mathbf{^7P_4}$ is (d) 840

Read more about permutation at:

https://brainly.com/question/1216161