Sum of the Digits is 2

[ArunangsuSahu]

Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?

(A) 6
(B) 7
(C) 14
(D) 5
(E) None Of These

[Anurag@Gurome]

Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?

Sum of digits of a number can be 2 only if either it is made of only one 2 and rest zeroes or two 1s and rest zeroes.

Number of such numbers between 1,000,000 and 10,000,000, i.e. such a seven digit number,

• 1. Two 1s and rest zeroes ---> Seven digit number starting with 1 and the other 1 can be in any other 6 places. Hence 6 such numbers.
  2. One 2 and rest zeroes ---> Seven digit number starting with 2. Only one such number is possible.

Hence, total number of such integers in the given range = (6 + 1) = 7

The correct answer is B.

[ArunangsuSahu]

Right..
6P1+1=7

[vaibhavgupta]

Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?

(A) 6
(B) 7
(C) 14
(D) 5
(E) None Of These

+1 for B!