Fulgour said:
To factor the total number of possible combinations
for twenty-two of something (anything?) it goes...
1x1= 1
2x1= 2
3x2= 6
4x6= 24
5x24= 120
6x120= 720
7x720= 5,040
etc., up to
22x...
*
But I've always wondered what the "equation" would
look like, you know, 10 to the power of or something?
What Fulgour writes is 22! (22 Factorial). It is actually the total number of 22 card spreads one could do. (The idea of a 22 card spread makes my head spin...)
http://www.mathwords.com/f/factorial.htm
http://www.mathwords.com/p/permutation_formula.htm Permutations is when the order matters. That is to say Death, Tower, Devil is not the same draw as Tower, Devil, Death.
http://www.mathwords.com/c/combination_formula.htm Combinations is when order doesn't matter. That is Death, Tower, Devil is considered the same as Tower, Devil, Death.
So if we want to know how many different 7 card draws there are out of 22 cards, and I'm pretty sure we'd all agree that order DOES matter, the formula is 22!/15! = 859,541,760.
If we really want to know what the total number of possible permutations from a 22 card deck [combinations in the quote before is wrong in mathematical terminology, since order DOES matter in draws], we'd have to sum up all of the possible spreads from 1 card spreads to the 22 card spreads.
22 card spreads 22!/0! = 1,124,000,727,777,607,680,000
21 card spreads 22!/1! = 1,124,000,727,777,607,680,000
20 card spreads 22!/2! = 562,000,363,888,803,840,000
19 card spreads 22!/3! = 187,333,454,629,601,280,000
18 card spreads 22!/4! = 46,833,363,657,400,320,000
17 card spreads 22!/5! = 9,366,672,731,480,064,000
16 card spreads 22!/6! = 1,561,112,121,913,344,000
15 card spreads 22!/7! = 223,016,017,416,192,000
14 card spreads 22!/8! = 27,877,002,177,024,000
13 card spreads 22!/9! = 3,097,444,686,336,000
12 card spreads 22!/10! = 309,744,468,633,600
11 card spreads 22!/11! = 28,158,588,057,600
10 card spreads 22!/12! = 2,346,549,004,800
9 card spreads 22!/13! = 180,503,769,600
8 card spreads 22!/14! = 12,893,126,400
7 card spreads 22!/15! = 859,541,760
6 card spreads 22!/16! = 53,721,360
5 card spreads 22!/17! = 3,160,080
4 card spreads 22!/18! = 175,560
3 card spreads 22!/19! = 9,240
2 card spreads 22!/20! = 462
1 card spreads 22!/21! = 22
The grand total of this is 3,055,350,753,492,663,521,764.
(Yes, I'm a math geek, and probability and statistics was my favorite course. I could write a whole other epic on the probability of any given draw occuring, but I don't want to
)
E. (who really hopes she doesn't get timed out of her login this time and have to type this all for a third time)