Question

The number of numbers of four different digits that can be formed from the digits of the number 12,356 such that the numbers are divisible by 4, is

• A. 36
• B. 48
• C. 12
• D. 24

Answer 1

Answer: (A)

36

For a number to be divisible by 4, the last 2 digits must be divisible by 4 (divisibility rule of 4)
So, the combinations of the last 2 digits of above numbers(1,2,3,5,6) that are divisible by are
$12,32,52,16,36,56$
and the first 2 digits are to be selected from the remaining 3 digits(the digits other than the ones n last 2 digits) and this can be done in ${}^3{\text{P}}_2=6$ ways
From above, there are six such cases with different last 2 digits
So, the total number of numbers$=6\times 6=36$