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Sum of the series(1*1!+2*2!+3*3!+.......................................+2012*2012!)

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TCS Other Question

A circular dart board of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point X in the circle. What is the probability that X is closer to the center of the circle than the periphery? Three dice are rolled. What is the probability that you will get the sum of the numbers as 10?