- #1

tellmesomething

- 223

- 21

- Homework Statement
- There are 4 boys and 4 girls. In how many ways can they sit in a row such that no two girls sit together.

- Relevant Equations
- Gah

I tried this for a long time but im not getting there, not even close. So far I tried finding out the total number of ways you could sit these boys and girls if there were no restriction, that came out to be 40320.

Then I found the number of ways you could have with two girls sitting next to each other, this came out to be 5040. Next I found out the number of ways you can seat them with 3 girls together which came out to be 2880. Then I found out the number of ways you can seat them with all of the girls together which came out to be 2880 again.

My plan was to add the latter up and subtract it from the total, soon enough I noticed that i'll be counting the 2 girls thrice in the addition and then the three girls twice. If this is even close to what the approach could be , please continue my train of thought and help me out here, if this is completely wrong please explain why so, and provide an alternate hint. Thankyou, have a nice day.

Then I found the number of ways you could have with two girls sitting next to each other, this came out to be 5040. Next I found out the number of ways you can seat them with 3 girls together which came out to be 2880. Then I found out the number of ways you can seat them with all of the girls together which came out to be 2880 again.

My plan was to add the latter up and subtract it from the total, soon enough I noticed that i'll be counting the 2 girls thrice in the addition and then the three girls twice. If this is even close to what the approach could be , please continue my train of thought and help me out here, if this is completely wrong please explain why so, and provide an alternate hint. Thankyou, have a nice day.