Question

Evaluate the following equation:

9P6


a. 60480
b. 60505
c. 60495
d. 60470

Answer 1

The answer is=A)60480

Answer 2

Answer:

Option: a is the answer.

a. 60480

Step-by-step explanation:

We are asked to find the value of:

$9_P_6$

where P represents the permutation i.e. the arrangement of 6 components out of the 9 components.

We know that a permutation of choosing r elements out of the n elements is calculated as:

$n_P_r=\dfrac{n!}{(n-r)!}$

Now, the value of $9_P_6$ is:

$9_P_6=\dfrac{9!}{(9-6)!}\\\\9_P_6=\dfrac{9!}{3!}\\\\9_P_6=\dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3!}{3!}\\\\9_P_6=9\times 8\times 7\times 6\times 5\times 4\\\\9_P_6=60480$

Hence, option a is the correct answer.

a. 60480