SOLUTION: So, I forgot how to do permutations/combinations. I'm embarrassed, but whatever. 8 places, 30 objects, how many combinations? Can you show me how?

Question 957472: So, I forgot how to do permutations/combinations. I'm embarrassed, but whatever. 8 places, 30 objects, how many combinations? Can you show me how?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We have 8 slots. Call them A through H

Slot A: 30 choices
Slot B: 29 choices (once you pick something for slot A, you can't reuse it)
Slot C: 28 choices
Slot D: 27 choices
Slot E: 26 choices
Slot F: 25 choices
Slot G: 24 choices
Slot H: 23 choices

Multiply out all the numbers: 30*29*28*27*26*25*24*23 = 235,989,936,000

So if you wanted to find the permutation P(30,8), then the answer would be 235,989,936,000

However, you want the combination, so you use the formula

C(n,r) = [ P(n,r) ]/[ r! ]

So that means...

C(n,r) = [ P(n,r) ]/[ r! ]
C(30,8) = [ P(30,8) ]/[ 8! ]
C(30,8) = [ 235,989,936,000 ]/[ 8*7*6*5*4*3*2*1 ]
C(30,8) = [ 235,989,936,000 ]/[ 40,320 ]
C(30,8) = [ 235,989,936,000 ]/[ 40,320 ]
C(30,8) = 5,852,925

So we got C(30,8) = 5,852,925

There are 5,852,925 different combinations (where order doesn't matter)

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Jim
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