Question

A business organization needs to make up a 6 member fund-raising committee. The organization has 10 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at most 1 accounting major is on the committee?

Answer 1

Answer:

Correct answer: 210 ways

Step-by-step explanation:

We will solve this using a combination without repetition  (n k) / k!

The total number of combinations is

(10  1) · (7  5) / 5! = 10 · (7  2) / 2! = 10 · (7 · 6)/ 2 = 10 · 42/ 2 = 10 · 21 = 210

God is with you!!!

Answer 2

Using the combination formula, it is found that the fundraising committee can be formed in 217 ways.

The order in which the members are chosen is not important, which means that the combination formula is used to solve this question.

Combination formula:

is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, the options are:

• 6 finance majors from a set of 7.
• 5 finance majors from a set of 7 and 1 accounting major from a set of 10.

Thus:

$T = C_{7,6} + C_{7,5}C_{10,1} = \frac{7!}{1!6!} + \frac{7!}{5!2!}\frac{10!}{1!9!} = 7 + 210 = 217$

The fundraising committee can be formed in 217 ways.

A similar problem is given at https://brainly.com/question/24437717