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A seven digit number is in form of abcdefg (g, f, e, etc. are digits at units, tens, hundred place etc.) where a < b < c < d > e > f > g. The number of such numbers are

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  1. 1981
  2. 2009
  3. 1560
  4. 1870

    Answer:The correct answer is: 1560Cases : i) If d = 6 then seven digit numbers possible are = 5C3. 3C3
    [as a,b,c can be choosen from 1,2,3,4 or 5 & similarly e,f,g can be choosen from the unused 2 digit which are less than 6 & 0 can be used]
    ii) If d = 7 then numbers possible =,6 straight C subscript 3 times to the power of 4 straight C subscript 3
    iii) If d = 8 then numbers possible = 7 C subscript 3 times to the power of 5 C subscript 3
    iv) If d = 9 then numbers possible = 8 straight C subscript 3 times to the power of 6 straight C subscript 3
    Add all cases

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