1) How many different four card hands can be dealt from a pack of 52 playing cards if at least one is an ace?
I thought there're 4 aces so it's just 4 * 51 * 50 * 49/4! but it's apparently 76145 .
2) Is there a fast way of finding all the four letter combinations of the word "mathematics"? So "math" is one, but "hatm" is the same one and while "mmat" is allowed "mmmt" isn't. I've managed to do this by case analysis (what happens when all letters are different and what happens when one letter repeats) and got 136 (which is right) but the method was long. Anyone know a fast way?