72.

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.