A 4 card hand is dealt from a standard 52card deck and then

A 4 card hand is dealt from a standard 52-card deck, and then one of the 4 cards is chosen at random. If the chosen card is a diamond, what is the probability that it is the only diamond among the 4 cards?

Solution

Number of ways to choose 4 cards is

C(52,4)

Number of ways to choose 4 cards with exactly one diamond is

C(13,1)C(39,3)

So required probablity is

[C(13,1)C(39,3)]/C(52,4)~0.439