How many decimal integers below 10^20 exist having sum of their digits less than 4?
We can consider 20-digit numbers with leading zeros allowed--just lop off any leading zeros for the final result, as there's still a 1-to-1 correspondence of numbers with leading zeros and a set of numbers with leading blanks.
Now if we know what the possible combinations of non-zero digits are, we can arrange them in the various positions.
The non-zero digits could be:
1
11, 2
111, 12, 3
These are the 6 possibilities. How many placement possibilities are for each of these combinatinos?
1: 20
11: C(20,2)= 190
2: 20
111: C(20,3)= 1140
12: P(20,2)= 380
3: 20
20+190+20+1140+380+20 = 1770
If we count zero, we can add 1 to the total.
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Posted by Charlie
on 2017-11-06 18:04:58 |
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