SOLUTION: Consider the word AARDVARK A) Determine all the permutations of all of the letters. B) Determine all the permutations of the letters in which the three A's are together

Algebra ->  Permutations -> SOLUTION: Consider the word AARDVARK A) Determine all the permutations of all of the letters. B) Determine all the permutations of the letters in which the three A's are together      Log On


   



Question 1159530: Consider the word AARDVARK
A) Determine all the permutations of all of the letters.
B) Determine all the permutations of the letters in which the three A's are together

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


YOU can determine all the permutations if you want.... I will only describe how to find the NUMBER of permutations.

A) All permutations....

There are 8 letters total; 3 are identical, and another 2 are identical. By a well-known counting principle, the number of permutations is

8%21%2F%28%283%21%29%282%21%29%29

B) If all three A's are together, treat them as a single "letter"; then there are 6 letters with just the two R's being identical. Again using the same counting principle, the number of permutations is

6%21%2F2%21