I want to know if I took 20 cards and laid them out, how many different ways I could lay the same cards out.?

Question

I'm looking for the mathematical formula as to how I can do this. I have 20 cards, all different. I want to know how many different combinations of cards there are.

Answer 1

there are 20! possible combinations. (20! = 1*2*3*4...*18*19*20)

Answer 2

I assume you mean how many possible sequences there could be, not how many shapes you could make or something like that.

Pretend there are 20 slots for the cards. You are holding the 20 cards. There are 20 different cards that could go into the first slot. After you put one in [doesn't matter which one], you will have nineteen possibilities for the next slot, then 18 for the next, and on until there's only one possibility for the last slot. So the equation would be:

20 x 19 x 18 x etc

Answer 3

20! = 20*19*18*...*2*1 = 2,432,902,008,176,640,000 ways.

The first card can be any of the 20 cards. Then from there, the next card can be any of the 19 remaining. The the third card can be any of the 18 remaining, and so on. Using the General Counting Rule, you would multiply these numbers to get 20!.

Answer 4

X=Number of Cards
N=X^2=Number of different ways of sorting the cards.
so, if X=20, then the answer will be: N=20^2=400
*Did You know? "If you want to choose R cards out of N cards, without being repetitive the answer will be:
N!/R!(N-R)! ("!" is the sign of factorial, e.g. 4!=1*2*3*4 so N! = 1*2*3*...*N-1*N)"