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Number of ways arranging 4 boys and 5 gi...

Number of ways arranging 4 boys and 5 girls if between two particular girls there is exactly two boys.

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Let four boys are `B_(1), B_(2), B_(3), B_(4)` and five girls are `G_(1), G_(2), G_(3), G_(4), G_(5)`.
Let two particular girls be `G_(1) " and " G_(2)` , between whom there is exactly two boys.
Two boys can be selected in `.^(4)C_(2)` ways.
Let these boys are `B_(1) " and " B_(2)`
Since boys `B_(1) " and " B_(2)` are between `G_(1) " and " G_(2)`, we have to arrange `(G_(1)B_(1)B_(2)G_(2)),G_(3),G_(4),G_(5),B_(3),B_(4)`.
Number of arrangements are `6!xx2!xx2!`.

So, total number of arrangements are `.^(4)C_(2)xx6!xx2!xx2!`.
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