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

Algebra
Tutor: None Selected Time limit: 1 Day

Time. A.1680 B.56 C.6720 D.109

Jun 11th, 2015

Thank you for the opportunity to help you with your question!


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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 11th, 2015

sorry i did for 3 instead of 5....let me do it now!

Jun 11th, 2015

6,720..........................................................

Jun 11th, 2015

Thank you so much for explaining!

Jun 11th, 2015

welcome dear!

Jun 11th, 2015

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