Question

How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits is not allowed?

Answer 1

the digits are to be arranged
_ _ _ _
a b. c. d (assigned position)
like this now
0 cannot be at 'a' as number will not be 4 digit
so 'a' can have 3 numbers (1,2,3)

now one digit out of 4 is used up and no restrictions except repetition so 'b' can have 3 possibilities
(0,1,2) if 3 is used or
(0,1,3) if 2 is used or
(0,2,3) if 1 is used
note that the three conditions above don't make up the possibilities but the fact that only 3 numbers can be used which is seen in coincidentally 3 ways

for 'c' 2 possibilities as 2 numbers are used
'd' can have only 1 digit left as 3 are used

summary
_ _ _ _
1,2,3. 0,1,2 (3 used). 0,1{ 2 used}. 0 [1 used]

so number of ways are
3*3*2*1=a*b*c*d=18