College Algebra, Chapter 10, 10.3, Section 10.3, Problem 30

A toddler has woo ten blocks showing the letters $C, E, F, H, N,$ and $R$. Find the probability that the child arranges the letters in the indicated order.

a.) In the order $FRENCH$.

There is only one correct arrangement of the letters in the order $FRENCH$. In the probability is defined as favorable outcomes divided by total outcomes. There are $6! = 720$ total arrangements. So the probability is $\displaystyle \frac{1}{720}$

b.) In alphabetical order

There are two arrangement of the letters in alphabetical order. The one is in ascending order and the other is in descending order. The probability is defined as a favorable outcomes divided by total outcomes. There are $6! = 720$ total arrangement. So the probability is $\displaystyle \frac{2}{720} = \frac{1}{360}$