Answer:
680
Step-by-step explanation:
Use the binomial coefficient where you choose [tex]k=3[/tex] numbers out of [tex]n=17[/tex] possible numbers and find the total amount of combinations since order does not matter:
[tex]\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{17}{3}=\frac{17!}{3!(17-3)!}\\\\\binom{17}{3}=\frac{17!}{3!(14)!}\\\\\binom{17}{3}=\frac{17*16*15}{3*2*1}\\\\\binom{17}{3}=680[/tex]
Thus, you can make 680 three-non-repeating-number codes
