Question

The number of distinct natural numbers up to a maximum of four digits and divisible by $5$ in which repetition of digits is not allowed is

• A. $1246$
• B. $952$
• C. $1106$
• D. None of these

Answer 1

The correct option is C $1106$

$\begin{array}{cccc}\text{Number}& \text{Numbers}& \text{Numbers}& \text{Total}\\ \text{of digits}& \text{ending with 0}& \text{ending with 5}& \\ \times & 0& 1& 1\\ \times \times & 9& 8& 17\\ \times \times \times & 9\cdot 8=72& 8\cdot 8=64& 136\\ \times \times \times \times & 9\cdot 8\cdot 7=504& 8\cdot 8\cdot 7=448& 952\\ & 585& 521& 1106\end{array}$