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  • 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.

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.

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best_answer

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

 

Posted by

Satyajeet Kumar

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