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Division and Distribution into Groups of Unequal Sizes

A committee o...

Question

A committee of 5 is to be formed from 6 boys and 5 girls,. The number of ways that the committee can be formed so that the committee contains at least one boy and one girl is

A

440

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B

445

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C

450

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D

455

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Solution

The correct option is D 455
Required number of ways = $6 c_{1} 5 c_{4} + 6 c_{2} 5 c_{3} + 6 c_{3} 5 c_{2} + 6 c_{4} 5 c_{1}$
= $30 + 150 + 200 + 75$
= $455$

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