Question

How many 5 card poker hands have exactly three face cards? How many have at least three face cards?

Answer 1

5 card poker

Standard deck consists of 52 cards.

There are 3 face cards for each suite. So there are total of 3*4=12 face cards in a deck.

Remaining 40 non face cards.

A)exactly 3 face cards?

We can select 3 face cards from 12 face cards in ways

So remaining 2 cards can be any of 40 non face cards . It can be selected in

Total number of poker hands = =220 * 780 = 171600

171600 poker hands have exactly three face cards.

B)at least 3 face cards

It means (exactly 3) +(exactly 4) +(exactly 5)

exactly 4

Number of ways= = 495*40 = 19800

For exactly 5 face cards

Number of ways= = 792*1 =792

Total number of poker hands that contains at least 3 face cards = 171600+19800+792= 192192

Total of 192192 poker hands.