A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repetition. Find the probability that the number formed is divisible by 4.

Explanation

The number of five digit numbers formed by digits 1, 2, 3, 4 and 5=5! =120
Now a no. is divisible by 4 iff the no. formed by the digits at tens and unit place in that order is divisible by 4. All possible two-digit numbers that can come in the end are
12, 13, 14, 15, 21, 31, 41, 51
23, 24, 25, 32, 42, 52
34 , 35, 43, 53
45,54
Out of these 20 numbers only four numbers 12, 32, 24 and 52 are divisible by 4. Following box shows the number of ways in which numbers can be filled.

`therefore` Number of numbers divisible by 4 `= 3!xx4=24`
The describe probability `=24/120=1/5`