Question

Which of the following is equal C(10,3)? a. C(3,10) b. C(10,7) c. P(10,3)

Answer 1

Answer:

B. C(10,7)

Step-by-step explanation:

Answer 2

Answer:

Option: b is correct.

b. C(10,7)

Step-by-step explanation:

The formula for C(n,k) is evaluated as:

$C(n,k)=\dfrac{n!}{k!\times (n-k)!}$

Also The formula for P(n,k) is evaluated as:

$C(n,k)=\dfrac{n!}{(n-k)!}$

$C(10,3)=\dfrac{10!}{3!\times (10-3)!}\\\\C(10,3)=\dfrac{10!}{3\times 7!}\\\\C(10,3)=120$

a)

$C(3,10)=\dfrac{3!}{10!\times (3-10)!}\\\\C(3,10)=\dfrac{3!}{10!\times (-7)!}$

and e know the factorial of negative number does not exist.

so, this  is not possible.

Hence, option a is incorrect.

b)

C(10,7)

$C(10,7)=\dfrac{10!}{7!\times (10-7)!}\\\\C(10,7)=\dfrac{10!}{7!\times 3!}\\\\C(10,7)=120$

Hence, option b is correct.

c)

P(10,3)

$P(10,3)=\dfrac{10!}{(10-3)!}\\\\P(10,3)=\dfrac{10!}{7!}\\\\P(10,3)=720$

Hence, option c is incorrect.

Hence, C(10,7) is equal to C(10,3).

Hence, option b is correct.