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.

We should find the number of possible ways the student can arrange 10 participants from total  40 volunteers. We should find the number of combinations.
Combination is a way of selecting r items (participants) from a set (collection) of n items (volunteers). The order of selection of the items does not matter in this situation. 
In our case: r=10 , n=40
The formula is: C=n!/(n-r)!*r!=40!/(30!*10!)=40*39*...*30!/30!*10*9*8*7**...*2=
40*39*...*31/10*9*8*7**...*2=4*39*...*31/9*8*7**...*2=847660528

I'd say d, none of the others make sense.