The number of seven digit integer is to be formed using only 1, 2 &amp;3 such that the sum of all the digits is 10. So how many such seven digit number is possible ?

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The number of seven digit integer is to be formed using only 1, 2 &amp;amp;3 such that the sum of all the digits is 10. So how many such seven digit number is possible ?

trutdelamodej0 · Accepted Answer

We start by listing the combinations of numbers that give us a digit sum of 10.We can have1,1,1,1,1,3,2And the number of different arrangements here is                     7        !                    5        !              =    42  Is the above sequence the only possible?Note that you need a certain number of 1&#039;s to make the number of digits 7 and the sum 10, because the number 2222222 has a digit sum of 14, for example. If we try other sequences, such as1,1,1,1,1,1,1,3We either get sequences that are more or less than 7 terms or that have a sum other than 10. I&#039;m not sure how to prove that the above sequence is the only one possible, so I&#039;ll leave that to other contributors.

The number of seven digit integer is to be formed using only 1, 2 &3 such that the sum of all the digits is 10. So how many such seven digit number is possible ?

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