In how many ways can 5 boys and 4 girls be arranged on a bench if
(a) If boys and girls are in separate groups

5760

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5755

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4329

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4000

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Solution

The correct option is A $5760$
The total number of ways of arranging 5 boys and 4 girls on a bench
$\to B o y s a n d G i r l s o r G i r l s a n d B o y s$
$= 5! \times 4! + 4! \times 5!$
$= 5! \times 4! \times 2$
$= 5760$

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In how many ways can 5 boys and 4 girls be arranged on a bench if (a) If boys and girls are in separate groups

The correct option is A 5760The total number of ways of arranging 5 boys and 4 girls on a bench →Boys and Girls or Girls and Boys =5!×4!+4!×5! =5!×4!×2 =5760

In how many ways can 5 boys and 4 girls be arranged on a bench if
(a) If boys and girls are in separate groups

The correct option is A $5760$
The total number of ways of arranging 5 boys and 4 girls on a bench
$\to B o y s a n d G i r l s o r G i r l s a n d B o y s$
$= 5! \times 4! + 4! \times 5!$
$= 5! \times 4! \times 2$
$= 5760$