A group of 4 friends are playing a card game using a standard deck of 52 cards. Each friend receives one card from the deck, and the next card is flipped up. Only one of the friend has a card that matches the suit of the flipped up card. What is the probability that only one person is able to have a suit that matches the suit of the card that's flipped up?
My work (it's most likely wrong):
Let's say that the turned up card is a hearts. There are 13 hearts in a deck of hearts.
13*39*38*37= 712,842
Only one of the cards is a hearts (13). The rest of the cards are not hearts (39, 38, 37).
The probability that one player has the matching suit -> 13/712,842.
The number is too small, and I feel that I did something wrong.
Three things:
With the card being flipped one of the $13$ hearts, the player whose card is a heart as well must have one of the $12$ remaining hearts, not $13$. So you must use a factor of $12$ not $13$
There are $4$ possible players whose card is a heart, so you need to have a factor of $4$ in there.
Most importantly, you should not be dividing by the factors of $12$, $39$, $38$, and $37$: these are the possible target combinations that go in the numerator. The denominator are all the possible ways to get $4$ cards to the $4$ players, so there you get something like $51$, $50$, $49$, and $48$
OK, using these hints, try again!