Question 520478
1.In how many ways can 4 girls and 3 boys be seated ina row if boys cannot sit together and girls cannot sit together? 
----
The 4 girls would have to be on both ends and the 3 boys interspaced.
Pattern: gbgbgbg
# of arrangements: 4!*3! = 144 
---------------------------------------------- 
2.In how many ways can 4 girls and 3 boys be seated in a row if girls must sit in the end seats? 
---
# of ways to fill the end seats: 4*3 = 12
# of ways to fill the other 5 seats: 5!
# of arrangements: 12*5! = 1440
---------------------------------------------- 
3.In how many ways can 4 girls and 3 boys be seated in a row if girls muct sit with girls and boys must sit with boys? 
---
You have 2 blocks to arrange: 2 ways
Girl block arrangements = 4! = 24
Boy block arrangements = 3! = 6
---
# of arrangements: 2*24*6 = 288
-----------------------------------------------
 
4.A driver is going from Natchitoches, LA to El Dorado, Arkansas by way of Shreveport. How many different routes can the driver make on their trip if they have 3 different routes from Natichtoches to Shreveport and five different routes from Shreveport to Eldorado?
--
# of routes: 3*5 = 15
=========================
Cheers,
Stan H.
=========================