Question

The number of distinct natural numbers up to a maximum of four digits and divisible by $5$, which can be formed with the digit $0,1,2,3,4,5,6,7,8,9$ each digit not occurring more than once in each number is

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

Answer 1

The correct option is C $1106$

Number of digits	Number ending with $0$	Numbers ending with $5$	Total
$x$	$0$	$1$	$1$
$xx$	$8$	$9$	$17$
$xxx$	$9.8=72$	$8.8=64$	$136$
$xxxx$	$\mathrm{9.8.7}=504$	$\mathrm{8.8.7}=448$	$953$
		Total	$1106$