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6 boys and 6 girls sit in a row at random. Find the probability that 1) The six girls sit together 2) The boys and girls sit alternatively.

6 boys and 6 girls sit in a row at random. Find the probability that 1) The six girls sit together
2) The boys and girls sit alternatively.

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
6 boys and 6 girls sit in a row at random.
Then, the total number of arrangements of 6 boys and 6 girls = arrangement of 12 people = 12!
(a) The girls sit together
When the girls sit together, all 6 girls can be grouped together and regarded as a single group. Hence we have 6 boys and 1 group of girls = 7 people
Hence, number of arrangements = 7!.
Now these 6 girls can be arranged among themselves = 6!.
The required probability = (6!.7!) /12!
= 1/132
(b) If the boys and girls sit alternatively
The required probability in that case would be given by
= 2 . 6! . 6!/ 12!
= 1/462.
Thanks & Regards
Latika Leekha
askIITians Faculty

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