4 times as many permutations

Question

explain why there are 4 times as many permutations of the word CARPET as compared to the word CAREER.

Answer 1

If you switch the 4th and 5 letters of CARPET, you get CAREPT

If you switch the 4th and 5 letters of CAREER, you get CAREER

 

Duplicate letters reduce the number of permutations you have by the factorial of the count of the duplicate letter.

 

In this case, two E's reduces the permutations by a factor of 2! = 2.

 

What else here reduces the number of permutations by a factor of 2?

 

In an extreme example, the number of permutations of MISSISSIPPI is reduced by 4! because of 4 S's, and 4! again because of 4 I's, and 2! because of 2 P's compared to an 11 letter word without repeated letters.