SOLUTION: The parents of 5 students are invited to attend their graduation ceremony. They are arranged to be seated in a row of 10 VIP seats. How many ways can they be seated if any 3 pairs

Question 1099798: The parents of 5 students are invited to attend their graduation ceremony. They are arranged to be seated in a row of 10 VIP seats. How many ways can they be seated if any 3 pairs of parents are to be seated to their own spouse.
ANS from tutorial bk : 403200 ( i just need to show steps )
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

(1) Choose the 3 pairs of parents out of the total of 5 pairs to be the ones that will be seated next to their spouses: C(5,3) = 10 {"5 choose 3").
(2)Treat each of the three pairs as units; then the number of ways of arranging those 3 units and the other 4 single parents is 7! = 5040.
(3) In each of the 3 pairs, the two spouses can be arranged in either of 2 ways: 2*2*2 = 8.

All together, the total number of ways of arranging the 10 people is .

IMPORTANT NOTE:

I used your given answer to get that result.

As the problem is written, I think the answer should be different -- because in many of the 7! arrangements of the 3 pairs of parents and the other 4 parents (step (2) above), other pairs of spouses will be seated next to each other. But the problem IMPLIES that EXACTLY 3 pairs of parents are supposed to be seated next to each other.

Counting the number of ways in that case would be far more complicated....
RELATED QUESTIONS
Ten students at graduation are in line to take their seats. How many ways can they be... (answered by jim_thompson5910)

Five men and their five wives were invited to a graduation ceremony for high school... (answered by 41 years)

Suppose that 85% of graduating students attend their graduation ceremony. A group of 15... (answered by Boreal)

There are 350 eighth-grade students at King Middle School. The Class President conducted... (answered by Fombitz)

Ten students are lined up to be seated. in how many ways can 5 students be seated in a... (answered by ewatrrr)

2 girls and 4 boys are to be seated in a row of 5 chairs. Find the number of ways they... (answered by ikleyn)

In a flag ceremony, the number of students in each row is 6 fewer than the number of... (answered by ankor@dixie-net.com)

in how many ways can 10 students be arranged in a row for a group picture? When they are... (answered by ikleyn)

10 students are lined up to be seated. in how many ways can 3 of them be seated in a row (answered by ikleyn)