Question

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?

Answer 1

  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 2

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:

$P_{n}^{r}=n^{r}$; where $n$ is the total number of elements, and $n$ is the subgroup.

Replacing values, we have:

$P_{77}^{3}=77^{3}=456,533$

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