Question

You volunteer to help drive children at a charity event to the zoo, but you can fit only 7 of the 18 children present in your van. how many different groups of 7 children can you drive?

Answer 1

The answer is 19,448 different groups, using the formula from permutation and combinations C (n, r) = (n!) / (r! (n-r)!) which calculates the number of times where r objects can be chosen from n object.

So,

C (17,7) = (17!) / (7! *(17-7)!)

C (17,7) = (17!) / (7! *10!)

C (17,7) = (17*16*15*14*13*12*11*10!) / (7! *10!) then eliminate 10!

C (17,7) = (17*16*15*14*13*12*11) / (7*6*5*4*3*2*1) = (98017920)(5040)

C (17,7) = 19,448 different groups