question.

aditya will you please tell me your solution.

let hemang first confirm the answer.

1. By similar process as Satyajit in for the cases having 24,12,32,52 are 72.
But in 2nd part 4 will divide the no. if it ends in 20,40 or 04. Then the no. of cases is 3(4_P3)=72.

So, total nos. are 72+72=144

de first 1ne is 144 as explained by arnab...
for de 2nd de no has to be both divisible by 4 nd by 3....
so sum of de digits of de 5 digit no shud be divisible by 3....
only cases are:
1)12345
last 2 digits can be 12,32,52 and 24 nd de first 3 digits can be arranged in 3! ways in each case.....so 24 ways....
2)12450
last 2 digits can be 12,24,20,40,04,52....numbers ending with 20,40,04 can be arranged each in 3! ways so 18 ways...
nos ending in 12,24,52 can be arranged each in 4 ways so 12 ways...
so total 54 ways.....

A number is divisible by 4 if its last 2 digits is divisible 4, which are 04,12,20,24,32,40,52.
The first 3 digits are the remaining digits excluding those with 0 as the first digit.
Total number is: 24*3+18*4=144.
A number is divisible by 12 if it is divisible by 3 and by 4.
A number is divisible by 3 if the sum of its digits is divisible by 3.
Last 2 digits 04 or 40, first 3 digits must be 1,2,5.
Last 2 digits 20 or 32, first 3 digits must be 1,4,5.
Last 2 digits 12, first 3 digits must be 0,4,5 or 3,4,5.
Last 2 digits 24, first 3 digits must be 0,1,5 or 1,3,5.
Last 2 digits 52, first 3 digits must be 0,1,4 or 1,3,4.
Total number is: 6*4+10*3=54
A number is divisible by 15 if it is divisible by 3 and by 5.
A number is divisible by 5 if its last digit is 0 or 5.
Last digit 0, first 4 digits must be 1,2,4,5.
Last digit 5, first 4 digits must be 0,1,2,4 or 1,2,3,4.
Total number is: 24+18=42