Question

Can someone help me use the combination formula?

Answer 1

There are 40 volunteers for the research study on the Power Pill. Each subgroup of the study will contain 10 participants. Determine how many ways these participants can be selected and explain your method.

Answer 2

And I know the answer is 847,660,528

Answer 3

https://prezi.com/gf0b680vvkuv/algebra-2-honors-project/

Answer 4

Delete all the tags and unnecessary crap so people see the question.

"40 volunteers for the research study on the Power Pill. Each subgroup of the study will contain 10 participants."

So from 40 people, choose 10. 40 choose 10.

40C10

Answer 5

The combination formula is:

Answer 6

Since we know that we need to work with \(40C10\), we can work with the formula.

Basically, 40 is \(n\) and 10 is \(r\) since \(nCr\).

Substitute those points back into the formula:
\[\large \frac{40!}{10! (40-10)!} = \frac{40!}{10! 30!}\]

Answer 7

Ohh, ok, makes sense. And then the exclamation mark means everything below that number, right? So like 40! = 40, 39, 38, 37...

Answer 8

Yep

You can either simplify, or plug into a calc

Answer 9

Ok, that's what I thought. Thanks so much, both of you!

Answer 10

Now that you guys helped with part 1, can you help with part 2? It uses a permutation instead of a combination.
@agent0smith
@calculusxy

Answer 11

There are 15 research doctors participating in the study and the research board needs to be established with the offices of director, assistant director, quality control analyst, and correspondent. (Doctors can only hold one office on the research board.) Determine how many ways this research board can be chosen and explain your process

Answer 12

And the answer for this one is 32,760

Answer 13

Since the positions are different, use permutations. From 15 you're putting 4 into an order (4 positions), so 15P4

Answer 14

Ok, and the formula for permutations is:

Answer 15

So the 15 is n, and the 4 is r right? Because "15P4" like you said @agent0smith

Answer 16

Yes, sorry got busy