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kotykmax [81]
2 years ago
8

A lock has a three number code made up of 17 numbers if none of the numbers are allowed to repeat how many different ways can yo

u choose three different numbers in order for unit code?
Mathematics
1 answer:
Marrrta [24]2 years ago
8 0

Answer:

680

Step-by-step explanation:

Use the binomial coefficient where you choose k=3 numbers out of n=17 possible numbers and find the total amount of combinations since order does not matter:

\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

Thus, you can make 680 three-non-repeating-number codes

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