The number of rational numbers lying in  the interval (2015, 2016) all whose digits after the decimal point are non-zero and are in decreasing order is

The number of rational numbers lying in  the interval (2015, 2016) all whose digits after the decimal point are non-zero and are in decreasing order is

  1. A

    i=199Pi

  2. B

    i=1109Pi

  3. C

    291

  4. D

    2101

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    Solution:

    A rational number of the desired category is  of the form 2015. x1x2xk and 9  x1 > x2 >  > xk  1. We can choose k digits out 9 in  9Ck

    ways and arrange them in de creasing order in just one way. Thus, the desired number of rational numbers is  9C1+9C2++  9C9=291 

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