Question

WILL GIVE BRAINLIEST!!!
Please help me understand this; it has something to do with Pascal's triangle
The prom committee will be made up of a group of 8 boys and girls. If there are 12 boys and 15 girls in the group to pick the committee from, how many ways can the committee be organized? 2220075 ways 3185325 ways 675675 ways 1860 ways?

Answer 1

So, let's multiply..

12 * 15 = 180

Then multiply again..

180 * 8 = 1,440

Then we add...

1,440 + 1,440 = 2,880

Then divide..
2,880 / 8 = 360...

It's actually 1,860 ways...
Not too many ways...

And you can correct me if I'm wrong..

I hope this helps you!

Answer 2

This is a combination problem and Pascal's Triangle is the result of combinations.

12C8×15C0 + 12C7×15C1 + 12C6×15C2 + 12C5×15C3 + 12C4×15C4 + 12C3×15C5 + 12C2×15C6 + 12C1×15C7 + 12C0×15C8 = 2220075

The first combination product represents the committee consisting of 8 boys and 0 girls.
The second combination product represents the committee consisting of 7 boys and 1 girl.
Do you see the pattern?