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A 0.67 C 0.067 D 0.08
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Solution
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Let the number be x1,x2,x3,x4
x1+x2+x3+...xr=n
The number of non-negative integral solution including zero will be
n+r−1Cr−1
For x1+x2=0 the no. of solution will be 1
x1+x2=1 no. of solution will be 2
x1+x2=2 no. of solution will be 3
Hence for x1+x2=n no. of solution will be n+1
Similarly for x3+x4=n no. of solution will be n+1
Hence no.of 4 digit no will be (n+1)2
Now for x1+x2=10,11,12,13,14...18 we have to consider
0≤x1≤9 and 0≤x2≤9
For 10, the answer will be the coefficient of x10 in the expansion of
(1+x+x2...x9)2
=11−2=9
Similarly for 11 it will be 8 and so on.
Hence corresponding to the number of lucky numbers we get
=(12+22+32...102)+(12+22+32...92)
=2(12+22+32...92)+102
=570+100
=670
The total number of integers between 0000 and 9999 are
10000.
Hence Probability will be 67010000
=0.067
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