Answer:
Option: b is correct.
b. C(10,7)
Step-by-step explanation:
The formula for C(n,k) is evaluated as:
[tex]C(n,k)=\dfrac{n!}{k!\times (n-k)!}[/tex]
Also The formula for P(n,k) is evaluated as:
[tex]C(n,k)=\dfrac{n!}{(n-k)!}[/tex]
[tex]C(10,3)=\dfrac{10!}{3!\times (10-3)!}\\\\C(10,3)=\dfrac{10!}{3\times 7!}\\\\C(10,3)=120[/tex]
a)
[tex]C(3,10)=\dfrac{3!}{10!\times (3-10)!}\\\\C(3,10)=\dfrac{3!}{10!\times (-7)!}[/tex]
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)
[tex]C(10,7)=\dfrac{10!}{7!\times (10-7)!}\\\\C(10,7)=\dfrac{10!}{7!\times 3!}\\\\C(10,7)=120[/tex]
Hence, option b is correct.
c)
P(10,3)
[tex]P(10,3)=\dfrac{10!}{(10-3)!}\\\\P(10,3)=\dfrac{10!}{7!}\\\\P(10,3)=720[/tex]
Hence, option c is incorrect.
Hence, C(10,7) is equal to C(10,3).
Hence, option b is correct.
