self Maths Puzzle

What is the value of 1×1!+2×2!+3!×3!+............n×n!;
where n! means n factorial or n(n−1)(n−2)...1?

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self Other Question

Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number? Three pipes A,B and C are connected to a tank. These pipes can fill the tank separately in 5hr, 10 hr and 15hr respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at (
3
4
)th of their normal rates for the 1st hour after which they supplied water at normal rate. Pipe C supplied water at (
2
3
)rd of its normal rate for 1st 2 hour, after which it supplied at its normal rate. In how much time, tank would be filled?