Determine the total number of non-negative integers containing not more than 41 decimal digits but having non-decreasing digits.

For example, 33455 is a valid instance of such integers while 98 is not.

Divide 41 into 10 parts, so each part is filled with a 
particular number.
=> x1+x2+x3+...+x10=41.(The number is x1 no. of 0's followed
by x2 no. of 1's followed by and so on finally followed by
x10 no. of 9's).
and 0 ≤ x1,x2,..,x10 ≤ 41.
No. of possible cases = Coefficient of x^41 in the 
expansion of (1-x)^(-10)=C(n+r-1,n-1)=C(10+41-1,10-1)
				     =C(50,9)

Edited on August 31, 2007, 4:08 am

Posted by Praneeth on 2007-08-31 03:46:54