Question

A state lottery game consists of choosing one card from each of the four suits in a standard deck of playing cards. (There are 13 cards in each suit.)

Count the number of ways in which four cards, each of a different face value, can be chosen.
ways

Answer 1

There are 17160 different ways to choose four cards, each of a different face value, from a standard deck of 52 cards. The calculation involves multiplying the number of options for each suit: 13 for clubs, 12 for diamonds, 11 for hearts, and 10 for spades.

Step-by-step explanation:

To count the number of ways in which four cards, each of a different face value, can be chosen from a standard deck of playing cards, we employ the fundamental counting principle. For each suit, there are 13 possible face values, and we need to choose one unique value for each suit.

Since each card must have a different face value, the process will involve the following steps:

Select a face value for the clubs card. There are 13 options.

Select a face value for the diamonds card that is different from the clubs card. There are 12 options remaining since one value is taken by the clubs card.

Select a face value for the hearts card that is different from both existing selections. Now, there are 11 options.

Select a face value for the spades card, ensuring it is different from the other three selections. This leaves us with 10 options.

Calculate the total number of ways using the counting principle: 13 × 12 × 11 × 10. Multiply these together to find the total number of ways: 17160.

Therefore, there are 17160 different ways to choose four cards where each has a unique face value from different suits.

Answer 2

17160

Step-by-step explanation:

first there are 13 options

then there are 13 - 1 that was chosen

then there are 13 - 2 that were chosen

then there are 13 - 3 that were chosen

so that's 13 options, then 12 options, then 11 options, and then 10 options

and in order to figure out all of the possibilties we mutiply the options so

13*12*11*10 = 17160

little further explaining of why this works:

we have a set of letters (3 in a set)

A B C

what are the possible combinations?

AB

AC

BC

BA

CA

CB

the answer is 6 which is also 3 * 2 * 1 = 6

HOPE THAT HELPS!1! ^_^