SOLUTION: yes how to solve: how many different 10 letter words (real or imaginary) can be formed from: s,f,s,m,z,s,f,a,i,n

Algebra ->  Permutations -> SOLUTION: yes how to solve: how many different 10 letter words (real or imaginary) can be formed from: s,f,s,m,z,s,f,a,i,n      Log On


   



Question 1052866: yes how to solve: how many different 10 letter words (real or imaginary) can be formed from: s,f,s,m,z,s,f,a,i,n
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 s,f,s,m,z,s,f,a,i,n

If the 3 s's and 2 f's looked different, maybe colored differently,
like this:

 s,f,s,m,z,s,f,a,i,n

then the number of distinguishable "words" would be 10!.

However there are many arrangements that we cannot tell apart 
because the 3 s's and 2 f's look just alike.

So we must divide the 10! by the product of the factorials
of the numbers of indistinguishable letters.

Since there are 3 indistinguishable s's and 2 indistinguishable f's,
we divide the 10! by 3!2!:

Answer: 10%21%2F%283%212%21%29%22%22=%22%2253628800%2F%286%2A2%2953628800%2F12%22%22=%22%22302400

Edwin