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  4. There are 10 monkeys. The total number of ways in which these monkeys can be seated around a round table so that exactly one monkey sits between 2 particular monkeys, is equal to

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Q. There are 10 monkeys. The total number of ways in which these monkeys can be seated around a round table so that exactly one monkey sits between 2 particular monkeys, is equal to

Permutations and Combinations

Solution:

Let 2 monkeys be $M _1 M _2$
$M _1- M _2 \rightarrow{ }^8 C _1$ (one can sit between them out of remaining 8)
Put - $M _1- M _2 \ldots \ldots \ldots \ldots \ldots$
Arrangement about round table
$={ }^8 C _1 \times 7 ! \times 2 ! \quad\left(2 !=\text { arrangement of } M _1 \& M _2\right)$