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Question

A team 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 and B should not be included in the same group is

A
420
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B
504
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C
714
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D
924
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Solution

The correct option is B 504
Total ways without restriction = 12C6× 6C6
Total ways when A and B are together = 2× 10C4× 6C6
Total required ways
= 12C6× 6C62× 10C4× 6C6=16![12×11×10!6×5×4!2×10!4!]=16![12×10!5×4!]=9×8×7=504

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