SOLUTION: How many distinguishable permutations can be made of the letters in the word STEGOSAURUS?

Algebra ->  Permutations -> SOLUTION: How many distinguishable permutations can be made of the letters in the word STEGOSAURUS?       Log On


   



Question 1095620: How many distinguishable permutations can be made of the letters in the word STEGOSAURUS?
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many distinguishable permutations can be made of the letters in the word STEGOSAURUS?
~~~~~~~~~~~~~~~~~~~~~~~

The given word contains  11  letters.


Of them, the letter S  is repeated 3 times,   and
         the letter U  is repeated 2 times.


The rest of the letters are unique.


So, the number of  distinguishable permutations  is  11%21%2F%283%21%2A2%21%29 = 3326400.

We divide the total number of permutations of 11! by 3!, because all permutations that permute the letter S only, lead to indistinguishable arrangements.

We divide the total number of permutations of 11! by 2!, because all permutations that permute the letter U only, lead to indistinguishable arrangements, too.


------------------
On Permutations, see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations
in this site.