SOLUTION: Using the letters A,M,O,S,U. We can form 120 five letter "words". If these "words" are arranged in alphabetical order, then what position the "word" USAMO occupies?

Algebra ->  Probability-and-statistics -> SOLUTION: Using the letters A,M,O,S,U. We can form 120 five letter "words". If these "words" are arranged in alphabetical order, then what position the "word" USAMO occupies?      Log On


   

Question 39270: Using the letters A,M,O,S,U. We can form 120 five letter "words". If these "words" are arranged in alphabetical order, then what position the "word"
USAMO occupies?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I come up with the 115th position in the list.
The list of 120 words is made up of:
24 words that start with "A"
24 words that start with "M"
24 words that start with "O"
24 words that start with "S"
24 words that start with "U"
5 X 24 = 120
"USAMO" occurs after 4 X 24 words, or after 96 words on the list
the 97th word is "UAMOS"
6 X 4 = 24 words that start with "U"
There are 6 words that start with "US"
There are 6 words that start with "UA"
There are 6 words that start with "UM"
There are 6 words that start with "UO"
The first word that starts with "US" is "USAMO"
So, the number on the list is:
96 + (3*6) + 1 = 96 + 19 = 115