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

User Generated

JubNzV

Mathematics

Description

Time. A.1680 B.56 C.6720 D.109

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

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.


Anonymous
Great study resource, helped me a lot.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags