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Question
The number of ways in which 5 boys and 3 girls can sit around a table so that all the girls are not to come together is:
The number of ways in which 5 boys and 3 girls can sit around a table so that all the girls are not to come together is:
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Solution
The correct option is D 4320
Number of ways in which 8 people can sit around a round table =(8−1)!=5040 ways
If three girls sit together, we consider it as 1 group and these three girls can sit in 3! ways.
So, number of ways in which in which 3 girls sit together in a circular permutation of 8 people is 3!5!=720.
Required number of ways in which no three girls sit together =5040−720=4320
Number of ways in which 8 people can sit around a round table =(8−1)!=5040 ways
If three girls sit together, we consider it as 1 group and these three girls can sit in 3! ways.
So, number of ways in which in which 3 girls sit together in a circular permutation of 8 people is 3!5!=720.
Required number of ways in which no three girls sit together =5040−720=4320
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