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How many natural numbers smaller than 10,000 are there in the decimal notation of which all the digits are different?

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Important Questions on Permutations and Combinations

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How many different 7-digit numbers are there, the sum of whose digits are odd?
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Six white and six black balls of the same size are distributed among ten urns so that there is at least one ball in each urn. What is the number of different distributions of the balls?
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How many different numbers which are smaller than 2.108 can be formed using the digits 1 and 2 only? 
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How many distinct 6 digit numbers are there having 3 odd and 3 even digits?
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How many 8-digit numbers are there the sum of whose digits is even?
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Amartya Banerjee has forgotten the telephone number of his best friend Abhijit Roy. All he remembers is that the number had 8-digits and ended with an odd number and had exactly one 9. How many possible numbers does Amartya have to try to be sure that he gets the correct number?
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How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4(if repetition of digits is allowed)?
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How many natural numbers less than4300  can be formed with the digits 0,1,2,3,4(if repeatations are not allowed)?