Question

A state lottery game consists of choosing one card from each of the four suits in a standard deck of playing cards. Each suit has 13 cards.

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

Answer 1

Answer: 17160

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