a game of cards is played with a hand that consists of 4 cards dealt from a deck of 44 cards how many different hands of cards are possible

Answer 1

To determine the number of different hands of 4 cards that are possible from a deck of 44 cards, we can use the combination formula.

The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items to choose from and r is the number of items to be chosen.

In this case, we have a deck of 44 cards, and we want to choose 4 cards for the hand. Plugging these values into the formula:

C(44, 4) = 44! / (4!(44-4)!)
= 44! / (4!40!)

Calculating this expression, it simplifies to:

C(44, 4) = (44 * 43 * 42 * 41 * 40!) / (4! * 40!)
= (44 * 43 * 42 * 41) / (4 * 3 * 2 * 1)
= (543,312) / (24)
= 22,638

Therefore, there are 22,638 different hands of cards possible from a deck of 44 cards.