Find the number of permutations of the first eight letters of the alphabet taking five letters at a

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JubNzV

Mathematics

Question Description

Time. A.1680 B.56 C.6720 D.109

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Explanation & Answer

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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

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New York University

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