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Rudik [331]
2 years ago
13

Elias was given a lock for his school locker. The lock contains numbers between

Mathematics
1 answer:
daser333 [38]2 years ago
6 0

Answer:

34,220

Step-by-step explanation:

Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:

\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220

Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.

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