The numbers 0 through 9 are to be 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, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?

Question

Quizplus · Accepted Answer

Since repetitions are not allowed and each code group consists of 4 unique digits selected from 0 through 9 (10 options), the number of different code groups can be calculated using the permutation formula for selecting 4 unique digits out of 10, which is 10P4 = 10! / (10-4)! = 10*9*8*7 = 5,040.

The Numbers 0 Through 9 Are to Be Used in Code