Question

The number of such numbers which are even (all digits are not different) is

• A. $404$
• B. $500$
• C. $380$
• D. None of these

Answer 1

Answer: (B)

$500$

For a number to be even it must have $0,2,4,6,8$ at the end.
Since it has to be a $4$ digit number, $0$ cannot be at the starting of the number.
Considering the number
$ABCD$
The number of ways of filling the first place will be $4$.
The number of ways of filling the second place will be $5$.
The number of ways of filling the 3rd place will be $5$
And the number of filling the 4th place will be $5$. Since repetition of the numbers are allowed.
Hence total number of permutations will be
$=4\times 5\times 5\times 5$
$=4\times 125$
$=500$.