A party program has four dances, two talk shows, three chorus, dance programs can not appear in a row, how many kinds of order of the program?
Question
A party program has four dances, two talk shows, three chorus, dance programs can not appear in a row, how many kinds of order of the program?
Solution
First, let's consider the dances as a single unit. So, we have 3 units: dances, talk shows, and chorus.
These 3 units can be arranged in 3! = 321 = 6 ways.
Within the dance unit, the 4 dances can be arranged in 4! = 432*1 = 24 ways.
However, since the dance programs cannot appear in a row, we need to place the other programs (talk shows and chorus) between them.
Consider the 4 dances as D1, D2, D3, D4 and the other programs as X. We can arrange them like this: D1 - X - D2 - X - D3 - X - D4.
There are 3 slots for the other programs (talk shows and chorus) between the dances. The 5 other programs (2 talk shows and 3 chorus) can be arranged in these 3 slots in 5P3 ways.
5P3 = 5! / (5-3)! = 543 = 60 ways.
So, the total number of ways to arrange the program is 6 (ways to arrange the units) * 24 (ways to arrange the dances within the dance unit) * 60 (ways to arrange the other programs between the dances) = 8640 ways.
Similar Questions
A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 5 freshmen, 9 sophomores, 8 juniors, and 8 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
The student council is putting on a school talent show. Sam, Ellie, Tim, and Jake have each signed up to perform. In how many different orders can the program be arranged?
Mark is getting a piñata for his birthday party. The 4 children at the party are going to take turns trying to break it open. If each child gets one turn, in how many different orders could the children take turns?
There are 3 women and 8 men signed up to join a swing dance class. In how many ways can the instructor choose 4 of the people to join if more than 1 must be men?(If necessary, consult a list of formulas.)
Last Tuesday, a music school held a dance concert and a pop concert at the same time. A total of 574 people attended the concerts. If 327 people were at the dance concert, how many people were at the pop concert?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.