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P & C

by jogi1984 » Wed Sep 21, 2011 8:32 pm
In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?

1,008
1,296
1,512
2,016
2,268
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by cans » Wed Sep 21, 2011 8:40 pm
A,B,C before F,G,H
Arrange A,B,C: 3! = 6 ways
arrange F,G,H: 3! = 6 ways
now select any one combination and there are 7 spaces. select 1 and place D.
now 8 spaces, place e: 8c1
and = 6*6*7*8 = 2016
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by shankar.ashwin » Wed Sep 21, 2011 9:27 pm
There are eight slots for the eight people here;

_ _ _ _ _ _ _ _

First try to place people who have no restrictions on their position, in this case D & E.

D can take any of the 8 seats here and E could take any of the remaining 7 positions ;

After D & E are seated, you have 6 positions left, in this ABC should occupy the first 3 slots and FGH should occupy the last 3 in any order.

ABC can sit in 3! ways, similarly FGH can sit in 3! ways;

So in total; 8*7*3!*3! = 2016
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