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
B
4120
C
4220
D
4320

Solution

## The correct option is D $$4320$$Number of ways in which 8 people can sit around a round table $$=(8-1)! =5040$$ waysIf 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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