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In how many ways 4 boys and 6 girls be s...

In how many ways 4 boys and 6 girls be seated in a line so that no two boys may sit together ?

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First arrange the 6 girls in a row.
This can be done in 6! Ways.
Once this is done, we have 7 places for 4 boys so that no two boys are together. This can be done in `.^(7)P_(4)` ways.
`therefore` Required arrangements `= .^(7)P_(4)xx 6 !`
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