How many different 5 card hands can be dealt from a deck of 52 cards? The order of the cards does not matter in this case.

Answer 1

The number of different 5 card hands that can be dealt from a deck of 52 cards can be calculated using the combination formula. The combination formula is given by:

C(n, r) = n! / (r!(n-r)!),

where n is the total number of items and r is the number of items chosen. In this case, n = 52 (total number of cards) and r = 5 (number of cards chosen).

So, the number of different 5 card hands can be calculated as:

C(52, 5) = 52! / (5!(52-5)!
= 52! / (5! * 47!)
= (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1 * 47!)
= 2,598,960.

Therefore, there are 2,598,960 different 5 card hands that can be dealt from a deck of 52 cards.