The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the…
The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is
802
602
702
1106
Solution
Natural numbers less than 10000 which are devisible by 5 , will be the numbers upto 4 digits which ends with zero or 5.
Number of all natural numbers upto 4 digits which ends with zero when no digits are repeated
$
=(9)(8)(7)(1)+(9)(8)(1)+(9)(1)=585
$
(Note that zero will not be counted as $0 \notin \mathbb{N}$ )
Number of all Natural number 5 upto 4 digits which ends with 5 when no digits are repeated.
$
=(8)(8)(7)(1)+(8)(8)(1)+(8)(1)+(1)=521
$
Therefore, required number of Natural number
$
=585+521=1106
$