Question
In how many ways will a team of 5 people be selected among 12 people such that one specific person will always be selected, and one specific person will always remain?
Solution
 If a specific person is always selected, then there will be no total selection left as per the question. If the person is never selected, then he will be removed from all numbers. Total persons = 12-2= 10 People to be selected = 10C4 =10 ! / (10-4)! ×4! =10 ! /6! ×4! =10×9×8×7×6!)/4! ×6! =10×9×8×7)/4×3×2 =10×3×7=210.
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