Question

How many ways are there to deal hands of five cards to each of six players from a deck containing 48 different cards

Answer 1

Using the combination formula, it is found that there are $6.4 \times 10^{32}$ ways to deal the cards to the six players.

The order in which the cards are handed to each player is not important, hence the combination formula is used to solve this question.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem:

• For the first player, 5 cards are taken from a set of 48.

• For the second player, they are taken from a set of 43.

• For the third for a set of 38, for the fourth from a set of 33, for the fifth from a set of 28 and for the sixth from a set of 23, hence:

$T = C_{48,5} \times C_{43,5} \times C_{38,5} \tims C_{33,5} \times C_{28,5} \times C_{23,5}$

$6.4 \times 10^{32}$

There are $6.4 \times 10^{32}$ ways to deal the cards to the six players.

More can be learned about the combination formula at brainly.com/question/24372153

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