There are 40 volunteers for the research study on the Power Pill. Each subgroup of the study will contain 10 participants. Determine how man

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.

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If we're just talking about selecting only one subgroup of 10, then we have the number of ways that we can choose 10 people from 40. This is known as a "combination," and is denoted as 40C10 or as C(40,10).

And C(40,10) = 847,660,528 ways   (quite a lot, huh??)

Now, if you're specifying that we're choosing one group of 10 from 40 and the next group of 10 from the remaining 30, and the next group of 10 from the remaining 20...we have WAY more options....this is given by

C(40,10) X C(30,10) X C(20,10) = 4,705,360,871,073,570,227,520 ways... (This number ≈ 4.7 "septillion," as  the term is used in the U.S.)

Note that I didn't have to worry about specifying in the "formula" the combination for choosing the last 10. There's only one way to do that........"choose" all of them!!!

Hope that answers your question   

Hmm!  Chris, suppose there are 4 volunteers where each subgroup consists of 1 participant. 

If there is one subgroup then clearly there are 4 possible choices.

However, if there are 4 subgroups, it seems to me there is only one way to do this; but your method would give nCr(4,1)*nCr(3,1)*nCr(2,1) = 24 ways!!  This would only be correct if each subgroup were given a different label and it was the number of combinations of label and participant that was required.  Perhaps the subgroups are given labels - this would be quite sensible. However, it isn't clear to me that that was what was intended here.

I'm not actually sure what was intended either, Alan.  I assumed that we were either selecting some 10 from the 40 or that we were selecting one group of 10, then another group of 10, etc.

Your way sounds valid, too!!

(Maybe we should form a "subgroup" of  "n" forum members to study the question!!

I wonder how many ways we could select THAT??)