SOLUTION: find the number of permutations of the first 8 letters of the alphabet for each situation. taking all 8 letters at a time

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Question 94372: find the number of permutations of the first 8 letters of the alphabet for each situation. taking all 8 letters at a time
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Since order does matter, we must use the permutation formula:




n%21%2F%28n-r%29%21 Start with the given formula



8%21%2F%288-8%29%21 Plug in n=8 and r=8



8%21%2F0%21 Subtract 8-8 to get 0



Expand 8!
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F0%21



Expand 0! to get 1
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%281%29




8%2A7%2A6%2A5%2A4%2A3%2A2%2A1 Simplify




40320 Now multiply 8*7*6*5*4*3*2*1 to get 40,320


So 8 choose 8 (where order does matter) yields 40,320 unique combinations

Answer by stanbon(48545) About Me  (Show Source):
You can put this solution on YOUR website!
8P8 = 8! = 40,320
--------
Cheers,
Stan H.