In how many different ways can all the letters of the word zookeeper be arranged?

The 9! ways of arranging the letters in ZOOKEEPER have to be divided by 2! and 3! the reason being that having fixed the positions of the non-repeated letters, the O's may be arranged in 2! ways and the E's in 3! ways without making a different word:

The answer is: 30,240 ways.