Question 520478: Can you please help me to understand if I am doing this correctly?
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? 4*3=12?
2.In how many ways can 4 girls and 3 boys be seated in a row if girls must sit in the end seats? 4!*3!=144?
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? 4*3=12?
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?
Thanks,
Rebecca
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
1. It depends. is it just 4 girls and three boys, or is it Mary, Alice, Suzy, and Jane plus Tom, Dick, and Harry? In the first case there is only one way: gbgbgbg. But in the second case there are 4! ways to arrange the girls times 3! ways to arrange the boys.
John
My calculator said it, I believe it, that settles it
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! 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?
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The 4 girls would have to be on both ends and the 3 boys interspaced.
Pattern: gbgbgbg
# of arrangements: 4!*3! = 144
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2.In how many ways can 4 girls and 3 boys be seated in a row if girls must sit in the end seats?
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# of ways to fill the end seats: 4*3 = 12
# of ways to fill the other 5 seats: 5!
# of arrangements: 12*5! = 1440
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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?
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You have 2 blocks to arrange: 2 ways
Girl block arrangements = 4! = 24
Boy block arrangements = 3! = 6
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# of arrangements: 2*24*6 = 288
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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?
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# of routes: 3*5 = 15
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Cheers,
Stan H.
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