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Q.

A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. The number of ways in which they can be seated if all the sisters are to sit together is 

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a

576

b

720

c

5040

d

144

answer is B.

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Detailed Solution

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3 sisters can be considered as one object and 4 brothers can be considered as four objects. Thus there are 5 objects. These objects can be arranged in 5! ways. 3 sisters can be permuted among themselves in 3! ways. Number of arrangements = 5! 3! = 120 x 6 =720.

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A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. The number of ways in which they can be seated if all the sisters are to sit together is