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)5,040
B)620
C)10,200
D)120

Question

Quizplus · Accepted Answer

Since repetitions are not allowed and each code group consists of 4 digits selected from 0-9 (10 options), the number of different code groups can be designed 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 Used in Code Groups