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

There are 456,533 ways to use the lock.

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.

Answer 2

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.