I had answered this question here
The notation C(n,r) is essential to the type of question you asked
by definition it is equal to n!/((n-r)!r!)
so for something like C(5,2)
it would be 5!/(3!2!) = 5x4x3x2x1/(2x1x3x2x1)
notice we can cancel
= 5x4/(2x1) = 20/2 = 10
you should have a key on your calculator that does this,
often it is called n C r
to do C(5,2)
press 2nd n C r
you should get 10
for your C(25,8) it means choose 8 people from 25.
Your are dealing with combinations, where the order in which the people are chosen does not matter.
See if you can make out the different answers I gave you and how they match up with the question.
e.g. for e), since we know 3 definite people are in the group we only need 5 more for team A, but the choice for that is from the other 22 available.
that leaves 17, and we need 3 of those for team B
finally leaving the remaining 14 to form team C
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