A family of 4 brothers and 3 sisters is to be arranged in a row, for a photograph. In how many ways can they be seated, if (i) all the sisters sit together. (ii) all the sisters are not together.

Answers (1)

i) consider all sisters as one bundle,
then we have a total of 5 elements,
which can be arranged in 5! ways=120 ways
and in the sisters case,three sisters,can be arranged in 6 ways
∴Total permutation =120×6 =720 ways

ii) NO sisters  sit together
* S * S * S *
The number of ways is
A and B together 10 cases.
Now come to permutation. 4 brothers in 4! ways and 3 sisters in 3! ways.
Total =10 * 4 ! * 3 !=1440 ways

 

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