College Algebra, Chapter 10, 10.3, Section 10.3, Problem 62

A researcher claims that she has taught a monkey to spell the word $MONKEY$ using the five wooden letters $E,O,K,M,N,Y$. If the monkey has not actually learned anything and is merely arranging the blocks randomly, what is the probability that he will spell the word correctly three consecutive times?

There is only one correct arrangement of the letters in the order $MONKEY$. The probability is defined as favorable outcomes divided by total outcomes divided. To get the probability that the monkey will spell the word correctly in three consecutive times is $\displaystyle \frac{1}{6!} \times \frac{1}{6!} \times \frac{1}{6!} = \left( \frac{1}{6!} \right)^3 = \frac{1}{373,248,000}$