Question

17. How many four-card hands can be dealt from a 52-card deck?

Answer 1

There is a pack of 52 cards and it is required to find the total number of 4 card hands that can be dealt.

So 4 cards needs to be selected out of 52.

Hence the total number is given by:

`\begin{gathered} _(52)C_4=(52!)/(4!(52-4)!) \\ =(52*51*50*49*48!)/(4*3*2*48!) \\ =270725 \end{gathered}`

Hence the total number of four card poker hand is 270,725.