The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is

Question

Aicharya · Accepted Answer

Let the number be
$\begin{aligned}
& 2 a b, a+b=13 \\ & \Rightarrow a, b \in\{0,9\} \\ & \Rightarrow 6 \text { numbers }\{(9,4),(8,5) \ldots(4,9)\}
\end{aligned}$
Similarly, for $3 a b, a+b=12 \Rightarrow 7$ numbers
For $4 a b, a+b=11 \Rightarrow$ Numbers
For $5 a b, a+b=10 \Rightarrow 9$ numbers
For $6 a b, a+b=9 \Rightarrow 10$ numbers
For $7 a b, a+b=8 \Rightarrow 9$ numbers
For $8 a b, a+b=7 \Rightarrow 8$ numbers
For $9 a b, a+b=6 \Rightarrow 7$ numbers
$\therefore$ Total ways $=64$.

The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is

Solution