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

Answer:

b. C(10, 7)

Step-by-step 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.

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Answer 2

Answer:

C(10,7)

Step-by-step 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)=$\frac{10!}{3!(10-3)!}$

By using combination formula: $nC_r=\frac{n!}{r!(n-r)!}$

$C(10,3)=\frac{10!}{3!7!}$

a.C(3,10)

We have n=3, r=10

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

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

b.C(10,7)

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

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

c.P(10,3)

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

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

Therefore, C(10,3)$\neq P(10,3)$

Answer:C(10,7)