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A combination lock uses three numbers between 1 and 78 with​ repetition, and they must be selected in the correct sequence. which of the five counting rules is used to find that​ number? how many different​ "combinations" are​ possible? is the name of​ "combination lock"​ appropriate? if​ not, what other name would be​ better?

Respuesta :

tramserran

  first number      and       second number       and     third number   =     Total

78 possibilities      x         78 possibilities           x     78 possibilities   =     234

Since "order" matters, this is a permutation.

So, this can be calculated using: ₇₈P₃

"Permutation lock" would be a more appropriate name.

Answer:

There are 456,533 ways to use the lock.

Step-by-step explanation:

According to the problem, the lock uses three numbers between 1 and 78, that is, 77 elements in total, with repetition. To find the answer we have to use the definition that allow elements to repeat, which is:

[tex]P_{n}^{r}=n^{r}[/tex]; where [tex]n[/tex] is the total number of elements, and [tex]n[/tex] is the subgroup.

Replacing values, we have:

[tex]P_{77}^{3}=77^{3}=456,533[/tex]

Therefore, there are 456,533 ways to use the lock.

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