There are 30 calculators, four of which need to be recharged. An instructor takes 25 of the 30 calculators to his statistics class. How many samples of 25 calculators contain exactly three calculators that need to be charged?

Question

anonymous · Answer

FYI the answer is in C(X,Y) form, not a whole number

agent0smith · Answer

From 4 calculators, if there's 4 needing recharging, the other 26 don't need recharging.

If he gets 3 needing recharging, then he must get 22 that don't need recharging (he's taking 25 calculators total).

From four of the calculators that need to be recharged, choose 3, multiply by from the 26 calculators, choose 22.
$$\Large 4C3 \times 26C22$$