Question

Which of the following is equal C(10,3)?

a. C(3,10)

b. C(10,7)

c. P(10,3)

Answer 1

B. C(10,7)

Explanation:

Answer 2

Option: b is correct.

b. C(10,7)

Explanation:

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

`C(n,k)=(n!)/(k!* (n-k)!)`

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

`C(n,k)=(n!)/((n-k)!)`

`C(10,3)=(10!)/(3!* (10-3)!)\\\\C(10,3)=(10!)/(3* 7!)\\\\C(10,3)=120`

a)

`C(3,10)=(3!)/(10!* (3-10)!)\\\\C(3,10)=(3!)/(10!* (-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)=(10!)/(7!* (10-7)!)\\\\C(10,7)=(10!)/(7!* 3!)\\\\C(10,7)=120`

Hence, option b is correct.

c)

P(10,3)

`P(10,3)=(10!)/((10-3)!)\\\\P(10,3)=(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.