Question

A four digit no. Is to be formed by numbers(0,2,4,6,8).Find number of such numbers which are divisible by 2 or 5 when repetition is allowed ? Thanks

Answer 1

500 different numbers can be formed.

Explanation:

Think of it as 4 empty places to fill, because we have to make a four digit no..

For the first place we 4 choices( 2,4,6,8), we can't select 0, because then it'll be a 3 digit no.

For second, third and fourth place we have all the 5 choices each (0,2,4,6,8). All are even digits, so we can use all of them in the last place as well; the no. would be divisible by 2.(and 5 in the case of 0)
Keep in mind we could only do this because repetition is allowed.
Now by fundamental principle of counting, we multiply the choices:
455*5 = 500