Suppose 3 people are each dealt 2 cards from a standard deck of playing cards. In how many ways can the cards be dealt (order doesn’t matter) so that somebody gets at least one ace? (Answer: 727,830,720)
Here is my answer:
3 people ,each gets 2 cards: A = $\frac{52*51}{2}*\frac{50*49}{2}*\frac{48*47}{2}$/6
no one has ace: B = $\frac{48*47}{2}*\frac{46*45}{2}*\frac{44*43}{2}$/6
Final answer is A-B
but it is not equal to the given answer, can someone tell me where I got wrong? Thank you!
I divided them by 6 because I think the order of people does not matter so I divide the number of ways these 3 people can be ordered but it seems that the right answer didn't divide this 6.