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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:


A
4020
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B
4120
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C
4220
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D
4320
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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 $$=5040-720=4320$$

Maths

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