Question

How many numbers between 20 and 5000 can be formed by the digits 0,1,2,3,4,5?​

Answer 1

Answer:

The numbers are going to have 4 digits, so let’s look at every possible set of 4 digits that have a sum that’s divisible by 3 :

0,1,2,3

0,2,3,4

That’s it. Only 2 sets.

Numbers between 2000 and 5000 that can be formed with 0,1,2,3 :

The first digit can be only 2 or 3 . The remaining 3 digits can be arranged in 3P3=6 ways, so that makes a total of 6×2=12 numbers with this set.

Numbers between 2000 and 5000 that can be formed with 0,2,3,4 :

The same logic applies - the first digit can only be 2 , 3 , or 4 , and there are 6 numbers that can be formed for each of these. That makes a total of 6×3=18 numbers with this set.

So, the final answer is 12+18=30 numbers.