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Question
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is ______.
Options
`1/432`
`12/431`
`1/132`
None of these
Solution
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is `1/132`.
Explanation:
If all the girls sit together, then we consider it as 1 group
∴ Total number of arrangement of 6 + 1 = 7 persons in a row
= 7! and the girls also interchanged their places with 6! ways.
∴ Required probability = `(6!7!)/(12!)`
= `(6 xx 5 xx 4 xx 3 xx 2 xx 7!)/(12 xx 11 xx 10 xx 9 xx 8 xx 7!)`
= `1/132`.
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