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?
A) 5,040
B) 620
C) 10,200
D) 120
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The number of different code groups can be calculated by finding the number of permutations of 4 digits selected from 10 digits (0-9) without repetition. This is given by 10P4 = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040.

The Numbers 0 Through 9 Are to Be Used in Code