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by Gavan » Mon Mar 12, 2012 8:25 am
In how many ways can you sit 8 people on a bench if 3 of them must sit together?
a) 720
b) 2,160
c) 2,400
d) 4,320
e) 40,320
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by Neo Anderson » Mon Mar 12, 2012 9:02 am
try doing it this way:
consider these 3 as one, thus you have to make 6 guys sit on a bench (6! ways)
now these three can be made to sit in different arrangements (3! ways)
total number of ways = multiple of both (6! X 3! ways)
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by Anurag@Gurome » Mon Mar 12, 2012 8:01 pm
Gavan wrote:In how many ways can you sit 8 people on a bench if 3 of them must sit together?
a) 720
b) 2,160
c) 2,400
d) 4,320
e) 40,320
Let the 8 people are A, B, C, D, E, F, G, and H.
Let us assume that A-B-C sit together, so let us consider them as 1 person. Now, we have 6 persons in all: A-B-C, D, E, F, G, and H.
These 6 persons can be seated in 6! ways.
Also A, B, and C can be arranged among themselves in 3! ways.
So, required number of ways = 6! * 3! = 6 * 5 * 4 * 3 * 2 * 1 * 3 * 2 = 4,320

The correct answer is D.
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