Question

A four digit number is formed using the digits $0,1,2,3,4$ without repetition. Find the probability that it is divisible by $4$

Answer 1

Total $4$ digit numbers formed
$4\times 4\times 3\times 2=96$
Each of these $96$ numbers are equally likely & mutually exclusive of each other.
Now, A number is divisible by $4,$ if last two digits of the number is divisible by $4$
Hence we can have the following numbers in the last two digits

0

4:

first two places can be filled in $3\times 2=6$ ways

1

2:

first two places can be filled in $2\times 2=4$ ways

2

0:

$6$ ways

2

4:

$4$ ways

3

2:

$4$ ways

4

0:

$6$ ways
Total number of ways$=6+4+6+4+4+6=30$ ways
probability$=\frac{favorableoutcomes}{Totaloutcomes}=\frac{30}{96}=\frac{5}{16}$