Answer to Question #96829 in Statistics and Probability for Brandyn Popejoy

Question

How many different​ 10-letter words​ (real or​ imaginary) can be formed from the following​ letters?
w,o,e,k,t,u,o,q,f,v

Answer 1

We can take one of 10 letters for first letter of word, then we can take one of 9 remaining letters for second letter of word, and so on.

We obtain $10\cdot 9\cdot\ldots\cdot 1=10!$ combinations of letters.

Since we have only two equal letters o, every combination we count twice. So we need to $10!$ divide by 2, and we obtain every combination, which is counted only one time.

Answer: $\frac{10!}{2}$