A total of 7 students (4 women and 3 men) participated in the math competition,
ID: 3316871 • Letter: A
Question
A total of 7 students (4 women and 3 men) participated in the math competition, and won 2nd place. Prof. Windley has asked each student on the team to demonstrate one type of problem that they were able to do correctly in the competition for the class the next day. If each student demonstrates only one problem, how many ways can their presentation be arranged in each of the following cases?
a) All women must present first?
b) A woman must perform first and a man must perform last?
c) The entire presentation will alternate between women and men?
Explanation / Answer
a) The 4 women can present in 4! ways followed by the 3 men in 3! ways.
Total number of ways = 4! * 3!
= 24 * 6
= 144.
b) The woman performing first can come in 4 ways and the man performing last can come in 3 ways.
The 5 in between can present in 5! ways.
Total number of ways = 4 * 5! * 3 = 1440.
c) The 3 men will present in between the 4 women.
The 4 women can present in 4! ways and the men in 3! ways.
Total number of ways = 4! * 3! = 24 * 6 = 144.
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