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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jun 11th, 2015
...
Jun 11th, 2015
Mar 28th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer