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Permutation problem
A family of 4 brothers and 3 sisters is to be arranged for a photo in a row. In how many ways they can be seated, if the sisters sit together.
Please solve this problem.
Replies (2)
First Consider all the sisters as a one member. Therefore total Members would be 5 ( 4 bros + 1) 5 members can be arranged in 5P5 ways and three sisters can be arranged in 3p3 ways therefore the total ways of arrangement will be
5P5 X 3P3 = 120 * 6 = 720 ways
4 brothers be arranged 4p4 ways = 4! = 4*3*2*1 = 24
3 sister be arranged if they sit together = 3p2*3p1 = 3!*3=3*2*1*3=18
therefore, total way = 24+18=42 ways.
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