How many different 4 card hands can be dealt from a deck of 52 cards? The...

How many different 4 card hands can be dealt from a deck of 52 cards? The order of the cards does not matter in this case.

Expert Solution

How many different 4 card hands can be dealt from a deck of 52 cards? The order of the cards does not matter in this case.

4 card hands can be dealt from a deck of 52 cards.

For the hands of cards, the cards dealt must be different, and the order in which they are dealt does not matter.

So, we are counting the number of combinations of 4 cards chosen from 52,

which gives 52C4

52C4 = ?

= 52 ! / ( 4! ) * ( 52-4)!

= 52! / ( 4 ! * 48 ! )

= 52 *51*50*49 * 48! / 4! * 48!

= 52*51*50*49 / 4 !

= 6497400 / 24

= 270725

Answer:- 270725

270725 different 4 card hands can be dealt from a deck of 52 cards

orchestra answered 2 years ago

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