Question

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

a. C(3, 10)
b. C(10, 7)
c. P(10, 3)

Answer 1

C(10,7)

Explanation:

We are given that C(10, 3)

We have to find the which is equal to C(10,3) in given options.

C(10,3)=
`(10!)/(3!(10-3)!)`

By using combination formula:
`nC_r=(n!)/(r!(n-r)!)`

`C(10,3)=(10!)/(3!7!)`

a.C(3,10)

We have n=3, r=10

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

It is not possible because n factorial is the product of n natural numbers.

b.C(10,7)

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

Therefore, C(10,7)=C(10,3)

c.P(10,3)

`P(n,r)=nP_r=\frac{n!(n-r)!}`

`P(10,3)=(10!)/((10-3)!)=(10!)/(7!)`

Therefore, C(10,3)
`\\eq P(10,3)`

Answer:C(10,7)

Answer 2

b. C(10, 7)

Explanation:

C(10, 3) = 10! / (3!)(10 -3)!

= 10!/3! 7!

C(10, 3) = 120

C(10, 7) = 10!/7!(10 - 7)!

= 10!/7!3!

C(10, 7) = 120

Therefore, the answer is b. C(10, 7)

Hope this will helpful.

Thank you.