A poker hand consisting of 4 cards is dealt from a standard

A poker hand consisting of 4 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 2 face cards.

Solution

A stamdard deck has 52 cards, out of which 12 are face cards (K, Q and J) and the rest 40 are not.

WE need to choose exactly 2 face cards and 2 non-face cards.

Thus,

required probability = ¹²C₂ * ⁴⁰C₂ /⁵²C₄

= 792 / 4165

= 0.1901

Hope this helps.