Question
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?
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?
Ask by Mathis King. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that Lupita goes first and her cousin goes fourth is
Solution
Step 1:
The total number of ways to arrange the 10 acts is
The total number of ways to arrange the 10 acts is
Step 2:
If Lupita goes first and her cousin goes fourth, then these positions are fixed. The remaining 8 acts can be arranged in the remaining positions in
If Lupita goes first and her cousin goes fourth, then these positions are fixed. The remaining 8 acts can be arranged in the remaining positions in
different ways.
Step 3:
Thus, the probability is the ratio of the favorable outcomes to the total outcomes:
Thus, the probability is the ratio of the favorable outcomes to the total outcomes:
Step 4:
Simplify the expression by writing
Simplify the expression by writing
Final Answer:
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Simplify this solution Extra Insights
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!
