You draw four cards from a standard deck, with replacement. How many possible hands are there where at least one card appears multiple times?
Here's what I have so far: to count the ways using the Fundamental Counting Principle it looks like 52*1*52*52 because you have 52 options for the first draw, only one option for the second draw so it matches the first, and then the third and fourth don't matter. But, now I think I need to divide because the order of the draws don't matter. Should I divide by 4 since the 1 above could be in 4 different positions? Should I divide by 4! since any 4 card hand can be arranged in 4! ways? But, what about the hands where the same card is repeated 3 times? Are those hands included in how I'm counting?
Is there a simple and organized way to keep track and count the possibilities?