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Q.

A reserve of 12 railway station masters is to be divided into two groups of 6 each one for day duty and the other for night duty. The number of ways in which this can be done if two specified persons A, B should not be included in the same group is

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a

500

b

504

c

730

d

600

answer is B.

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Detailed Solution

$A, B c a n b e i n d i f f e r e n t g r o u p s in 2 w a y s T h e r e m a i n i n g 10 p e r s o n s c a n b e d i v i d e d i n t o t w o g r o u p s c o n t a i n i n g 5 e a c h =^{10} C_{5} ∴ N o o f w a y s o f d i v i d i n g t h e m i n t o t w o g r o u p s = 2 x^{10} C_{5} \Rightarrow 2 (^{10} C_{5}) = 504$

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