SOLUTION: find the number of permutations of the first 8 letters of the alphabet for each situation. taking 3 letters at a time

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Question 94351: find the number of permutations of the first 8 letters of the alphabet for each situation. taking 3 letters at a time
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!



Since order does matter (this is because the word "cab" is different than "abc"), we can use the permutation formula:




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



8%21%2F%288-3%29%21 Plug in n=8 (this is number of letters given) and r=3 (this is the number of letters we can use together at a time)



8%21%2F5%21 Subtract 8-3 to get 5



Expand 8!
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F5%21



Expand 5!
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29



%288%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29 Cancel



8%2A7%2A6 Simplify




336 Now multiply 8*7*6 to get 336


So 8 choose 3 (where order does matter) yields 336 unique combinations