The total number of numbers, lying between 100 and 1000 that can be...

We need three digits numbers.

Since $1 + 2 + 3 + 4 + 5 = 15$

So, number of possible triplets for multiple of $15$ is $1 \times 2 \times 2$

so $= 4 \times ⌊ 3 + 4 \times 3 - 1 \times 2 \times ⌊ 2 = 32$

Alternate:

divisible by $5 =$$4 \times 3 = 12$

Divisible by $3$

$$\begin{array}{ll}12 \to 3, 4, 5 \to 3 ! = 6 \\ 15 \to 2, 3, 4 \to 3 ! = 6 \\ 24 \to 1, 3, 5 \to 3 ! = 6 \\ 42 \to 1, 2, 3 \to 3 ! = 6\end{array}$$24$</p><p>Divisible by$15$</p><p>$1, 4, 5; 4, 1, 5; 3, 4, 5; 4, 3, 5$</p><p>Required No.$= 24 + 12 - 4 = 32$