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- October 12, 2019 at 6:56 pm #39189amit poddarParticipant
Problem 19. How many ten-digit numbers have the sum of their digits equal to

a) 2;

b) 3;

c) 4?October 15, 2019 at 8:52 am #39327Jatin Kr DeyParticipantHello Amit, your question is not clear to us. Can you please send any photo of it?

October 15, 2019 at 4:39 pm #39347AParticipantFirstly, 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 10 months ago by A.

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