Yan was opening a new restaurant, so she went to the sign store to get letters to make a sign to hang above the storefront. When she got to the sign store, the only letters they had in stock were two copies of the letter 'X,' two copies of the letter 'E,' and one copy of the letter 'V.' Yan decided to buy all the letters and use all of them to make the name of her store. How many different names can she give her store using these 5 letters?
If there were 5 different letters, there would be 5! ways of arranging them.
However, since there were two copies of the letter X, we need to divide that answer by 2!.
And, since there were two copies of the letter E, we need to divide that answer by 2!.
5! / 2! / 2! = 120 / 2 / 2 = 30 different arrangements of the letters.