Question

The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted—in other words, the same number cannot be used more than once in a total sequence. As examples, 2,256; 2,562; or 5,559 would not be permitted. How many different code groups can be designed?

a. 10,200.
b. 120.
c. 620.
d. 5,040.

Answer 1

The first digit can be any of 10; the next, any of 9; the 3rd digit can be any of 8; and the last digit can be any of 7.

.. 10*9*8*7 = 5,040 . . . . different code groups

Explanation: