+612 For how many three-digit positive integers is the sum of the digits equal to 5
I get 8 as follows: {1, 0, 4} | |{1, 4, 0}{2, 0, 3}| {2, 3, 0} |{3, 0, 2} || {3, 2, 0} |{4, 1, 0} || {4, 0, 1}
+129852 The possible sums are
1+ 4 + 0
2+ 2 + 1
3 + 1 + 1
3 + 2 + 0
5 + 0 + 0
So....the possible integers are
104, 113, 131, 122, 140, 203, 212, 221,230, 302, 311, 320, 401, 410, 500
I get 15
+26393 For how many three-digit positive integers is the sum of the digits equal to 5
Three-digit integer: \(abc\)
\(\text{ $1\le a \le 5$ }\\ \text{ $0\le b \le 4$ }\\ \text{ $0\le c \le 4$ and $c=5-(a+b)$ } \)
\(\begin{array}{|c|c|c|c|c| } \hline & b=0 & b=1 & b=2 & b=3 & b=4 \\ \hline a=1 & c=4 & c=3 & c=2 & c=1 & c=0 \\ a=2 & c=3 & c=2 & c=1 & c=0 \\ a=3 & c=2 & c=1 & c=0 \\ a=4 & c=1 & c=0 \\ a=5 & c=0 \\ \hline \end{array} \)
15 possible integers
\(\begin{array}{ c c c c c } & 104 & 113 & 122 & 131 & 140 \\ & 203 & 212 & 221 & 230 \\ & 302 & 311 & 320 \\ & 401 & 410 \\ & 500 \\ \end{array}\)
