Six boys and 3 girls are to be seated at random in a row for a photograph. The probability that no two girls will sit together
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Given,
Total boys = 6
Total girls = 3
To Find,
The probability that no two girls will sit together =?
Solution,
Total possible outcomes = 10! / (7! * 3!) = 10C3
The number of ways in which no two girls will sit together will be the same as the number of ways out of 7 seats 3 seats are selected which is 7C3
So, The number of ways in which no two girls will sit together = 7C3
The probability that no two girls will sit together = 7C3 / 10C3
On simplifying this we get,
The probability that no two girls will sit together = 7 / 24
Hence, The probability that no two girls will sit together will be 7 / 24
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