How many 4-digit numbers are there if no digit is repeated?
Or
How many numbers are there between 1000 and 9999 so that no digit is repeated?
Number of digits available = 10
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Number of digits to be used = 4
Since the numbers are to be of four digits.
∴ 0 cannot be filled in box 1.
Number of permutations for box 1 = 9 ...(i)
Now, we have 9-digits and 3 boxes.
n = 9, r = 3.
Number of permutations = ...(ii)
From (i) and (ii), we have total number of permutations, by fundamentals principle of counting
= 9 x 504 = 4536.