Bunuel wrote:
How many integers between 1 and 10^21 are such that the sum of their digits is 2?
A. 190
B. 210
C. 211
D. 230
E. 231
Kudos for correct solution.
10^21 here we have two option
1. 1+1 = 2
2. 2+0 =2
Now for the first option ,
10^21 can be written as = 1,000,000,000,000,000,000,000 i.e 21 zero's
Here we have to fill two places with 1 out of 21 places i.e 11,1001,100001 ....(since the number has to be less than 10^21)
so we can use the combination formula as 21C2 as we are choosing two places from the 21 places of zero's
=210 ways.
Now for the option 2, choosing 2
we have 21 ways i.e 02,020,200,2000 ....(i.e we can fill up the 21 zero's places with 2,as the number has to be less than 10^21)
Therefore total no of ways =210+21=231 ways.
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