Explanation:

Let the six digit number be abcdef
'a' can take all values except 0 since it will not be a 6 digit number then. So this means it can take any of 5 values.
'b' can take one the remaining 5 digits.
'c' can take any of the remaining 4
Similarly 'd' can take 3, 'e' can take 2 and 5'f' can take 1 value
So this means the total numbers that can be formed are :
5*5*4*3*2*1 = 600
For the numbers divisible by 10:
The last digit should be always 0
In this case the total possibilities are: 5*4*3*2*1*1 = 120