Question

how many 5 digit numbers which are divisible by 6 can be obtained by using digits 0,1,2,3,4,5 (repeating is allowed)

Answer 1

The 5 digit numbers should have only digits 0,1,2,3,4 or 5.
Let the number be abcde.

First number with 5 digits divisible by 6: 10 002.
Last number with 5 digits divisible by 6:  55 554

Numbers with 100 as prefix:
  abc= 100.  de=02, 14, 20, 32, 44, 50
  abc= 101   de = 04, 10, 22, 34, 40, 52
  abc = 102  de = 00, 12, 24, 30, 42, 54
     :                :
  abc = 155   de=04, 10, 22, 34, 40, 52
So between 10000 to 19999 we have  156 * 6 = 936  numbers.

Similarly between 20000 to 29999 we have also 156 * 6 = 936 numbers.

Total number :   936 * 5 = 1, 680 

Answer 2

Answer:

The 5 digit numbers should have only digits 0,1,2,3,4 or 5. Let the number be abcde.

First number with 5 digits divisible by 6: 10 002. Last number with 5 digits divisible by 6: 55 554

Numbers with 100 as prefix: abc= 100. de 30214203244 50

abc= 101 de = 0410223440 52 abc = 102 de = 0012243042 54 : :

abc = 155 de3D 0410223440 52

So between 10000 to 19999 we have 156 * 6 = 936 numbers.

Similarly between 20000 to 29999 we = have also 156 * 6 = 936 numbers. Total number: 936 * 5 = 1, 680