problem sum

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    amit poddar

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


    Jatin Kr Dey

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



    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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