SOLUTION: how many three digit numbers have the sum of their digits equal to 22?

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Question 438433: how many three digit numbers have the sum of their digits equal to 22?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
None of the digits can be 3, 2, or 1, since
the sum of any arrangement of 399 is too small 3+%2B+9+%2B+9+=+21
What is left is all possible arrangements of:
994
985
976
886
877
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The arrangements are:
994
949
499 - 3 possible
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985
958
895
859
598
589 - 6 possible
---
976 - 6 possible
886 - 3 possible
877 - 3 possible
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There are 21 3-digit numbers whose digits add up to 22