Question
Tyrone, Eduardo, lan, and Maria have all been invited to a dinner party. They arrive randomly a
each person arrives at a difierent time.
a. In how many ways can they arrive?
b. In how many ways can Tyrone arrive first and Maria last?
c. Find the probability that Tyrone will arrive first and Maria last.
a.
b.
c.
each person arrives at a difierent time.
a. In how many ways can they arrive?
b. In how many ways can Tyrone arrive first and Maria last?
c. Find the probability that Tyrone will arrive first and Maria last.
a.
b.
c.
Ask by Wheeler Crawford. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. 24
b. 2
c. 1/12
b. 2
c. 1/12
Solution
-
There are 4 different people arriving at different times, so the total number of arrival orders is
-
If Tyrone arrives first and Maria arrives last, then the remaining 2 (Eduardo and Lan) can arrive in any order. This gives
-
The probability that Tyrone arrives first and Maria last is the number of favorable outcomes divided by the total number of outcomes:
a.
b.
c.
b.
c.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Mind Expander
To solve the problem, let’s start with part (a).
a. The number of ways Tyrone, Eduardo, Ian, and Maria can arrive can be determined by calculating the permutations of 4 people. This is given by
So the answer for part (a) is 24.
b. For part (b), we need to find the number of ways Tyrone can arrive first and Maria can arrive last. That leaves us with Eduardo and Ian who can arrive in any order in the two remaining time slots. The number of ways to arrange Eduardo and Ian is
So the answer for part (b) is 2.
c. For part ©, the probability that Tyrone will arrive first and Maria last can be found by dividing the number of favorable outcomes (2 from part b) by the total number of outcomes (24 from part a):
So the probability for part © is
Summarizing:
a.
b.
c.
a.
b.
c.
