Question

11. A club has 45 members and its membership committee has 7 members. How many different

Answer 1

Answer: $\Large\boxed{45379620}$

Step-by-step explanation:

Given information

Total members = 45

Number of membership = 7

Concept

Imagine that the membership is seating where people need to sit:

_____    _____    _____    _____    _____    _____    _____

For every position, there can be only 1 member, and 1 member can only be in one membership position, so there will not be the repetition of members.

Also, since order does not matter in assigning memberships, we use a combination

Given formula

$\dbinom{n}{r}=\dfrac{n!}{(n-r)!r!}$

$n=size~of~the~set\\r=number~of~selected$

Substitute values into the given formula

$\dbinom{45}{7}=\dfrac{45!}{(38)!7!}$

Simplify the fraction by canceling out repeating values

$\dbinom{45}{7}=\dfrac{45\times44\times43\times42\times41\times40\times39\times38!}{(38)!7!}$

$\dbinom{45}{7}=\dfrac{45\times44\times43\times42\times41\times40\times39\times\underline{38!}}{(\underline{38)!}7!}$

$\dbinom{45}{7}=\dfrac{45\times44\times43\times42\times41\times40\times39}{7!}$

$\Large\boxed{\dbinom{45}{7}=45379620}$

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

Answer:

45 379 620 ways

Step-by-step explanation:

45 C 7   = 45! / (7! 38!) = 45379620