Question

ONE MEDAL!! A 5 person committee will be comprised of 2 men and 3 women. If there are 6 men and 8 women in which to choose from, determine the number of different committees that could be formed. a.1,440 b.840 c.288 d.48

Answer 1

There are 6C2 possible combinations of men and 8C3 possible combinations of women. Each combination of men can be taken with each of the 8C3 possible combinations of women. Therefore the number of committees that can be formed is given by:
\[\frac{6!}{2!4!} \times\frac{8!}{3!5!}=you\ can\ calculate\]

Answer 2

The calculation can be simplified as follows:
\[\frac{6\times5\times8\times7\times6}{2\times3\times2}=you\ can\ calculate\]

Answer 3

how about the 4! can i calculate it tooo??

Answer 4

In the simplified calculation the 4! does not exist, the reason being it was divided into the 6! leaving 6 * 5. Similarly the 5! was divided into the 8! leaving 8 * 7 * 6. Do you understand?
You can calculate the answer using factorials if you want by going back to the first calculation.

Answer 5

@clamin Are you there?

Answer 6

yes

Answer 7

wait im calculating

Answer 8

i get it..so the answer is b.840?? right

Answer 9

Yes, your answer is correct. Good work :)

Answer 10

thanks..

Answer 11

You're welcome :)