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# problem sum

This topic contains 2 replies, has 3 voices, and was last updated by  A 1 month ago.

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• #39189

amit poddar
Participant

Problem 19. How many ten-digit numbers have the sum of their digits equal to
a) 2;
b) 3;
c) 4?

#39327

Jatin Kr Dey
Participant

Hello Amit, your question is not clear to us. Can you please send any photo of it?

#39347

A
Participant

Firstly, I assume that the question you asking is to find the number of 10-digit numbers whose digit sum is 2,3, and 4 respectively, in separate cases.

Subdivision (a) :- Digit sum is 2

We have that 2 = 0+2 or 1+1.

So we can either have a 10-digit number composed of only one 2 and nine 0’s, or a 10-digit number composed of two 1’s and eight 0’s.

In the first case, there is only one such number, that is 2000000000, and nothing else, because 2 can only be in the first digit’s place.

In the latter, we have a 1 to be in the first digit’s place and another 1 has 9 other places.

So totally, in this case we have 1 x 9 = 9 such numbers, and in the first case we have $1$ number, so totally there are 10 such numbers.

Similarly, you can follow this principle for the other two subdivisions too. Hope this helps.

• This reply was modified 1 month ago by  A.
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