Question

Frank has the face cards and aces of a deck of cards. How many permutations and combinations are there of these cards taken 4 at a time?

(Remember that a deck of cards has 4 suits each containing an ace, king, queen, and jack.)

Answer 1

@jim_thompson5910
I know I use these.

Answer 2

There are 12 face cards and 4 aces giving 16 different cards. Just substitute the values n = 16 and r = 4 in the formulas.
\[16P4=\frac{16!}{(16-4)!}=?\]
\[16C4=\frac{16!}{4!(16-4)!}=?\]

Answer 3

I don't know how to solve those equations...

Answer 4

Do you know what a factorial is? For example 3! = 3 * 2 * 1 and 5! = 5 * 4 * 3 * 2 * 1.
So 3! = 6
and 5! = 120
You might have a calculator that has the factorial function. Look for the exclamation sign.

Answer 5

Well 16! come up as 2.09228989E13

Answer 6

And 4!=24

Answer 7

Good work! My calculator gives the same results.
Keep in mind that (16 - 4)! = 12!
So for the permutations find 16! and divide by 12!.

Answer 8

So 43680

Answer 9

Correct! There are 43680 permutations of the 16 cards taken 4 at a time.
Now divide that answer by 4! to find the combinations>

Answer 10

10920

Answer 11

It was wrong.

Answer 12

Divide by 4!

Answer 13

Yes divide the permutations result by 4! to find the combinations.

Answer 14

You said 4. So I got the answer wrong the first time. Thanks for the help!

Answer 15

Your welcome :)
BTW the first posting for combinations calculation shows ".....divide that answer by 4! ......." on my computer.