How many five card hands consisting of 2 kings and 3 aces ca

How many five card hands consisting of 2 kings and 3 aces can be dealt from a deck of 52 playing cards? Answer: What is the probability that a five card hands consist ofs 2 kings and 3 aces? Answer:

Solution

Each deck of 52 Playing cards contains 4 Kings and 4 Aces.

2 Kings can be selected out of 4 in ⁴C₂ ways.

3 Aces can be selected out of 4 in ⁴C₃ ways.

Hence total no of 5 card hands consisting of 2 Kings and 3 Aces are: ⁴C₂ * ⁴C₃=6*4 =24

Probability that the 5 card hand consists of 2 Kings and 3 Aces is=

(total nmber of 5 card hands consisting of 2 Kings and 3 Aces)/(total number of 5 card hands )

=24/⁵²C₅ =1/108290