Lupita and her cousin are performing in separate acts in a
talent show. The talent show has 10 acts. Suppose the
talent show coordinator randomly selects the order of the
acts. What is the probability Lupita will go first and her
cousin will go fourth?

To find the probability that Lupita goes first and her cousin goes fourth in a talent show with 10 acts, we can follow this fun approach:

Since the order is randomly selected, the total number of possible arrangements of the 10 acts is 10!. Now, to find the specific case where Lupita is first and her cousin is fourth, we have 1 choice for Lupita, 1 choice for her cousin, and then we can arrange the remaining 8 acts in any order, which gives us 8! arrangements.

The probability is thus calculated as follows:

The probability = (Number of favorable outcomes) / (Total outcomes) = (1 * 1 * 8!) / 10! = 8! / (10 * 9 * 8!) = 1 / 90.

So, the probability that Lupita is first and her cousin is fourth is 1/90! How exciting is that!