Problema Solution

What is the theoretical probability of being dealt exactly three 4's in a 4-card hand from a standard 52-card deck?

Answer provided by our tutors

number of ways to get three 4's: 4C3 = 4


number of ways to get 1 non-4 cards: 48C1 = 48


number of ways to get three 4's in a 4-card hand = 4*48


number of ways to get 4 cards randomly: 52C4 = 52!/(4!(52 - 4)!) = 52!/(4!48!) = 49*50*51*52/(2*3*4) = 270725


P(exactly three 4's in a 4-card hand) = (4*48)/270725 = 0.0007092