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A combination lock has 7 digits. How many distinct combinations does this lock have if the numbers used have to be 0 through 5

Sagot :

Satsumaimo

Answer:

279,936

Step-by-step explanation:

Since there are 6 options for every digit, and seven digits

So,

6^7=279,936

The total number of  distinct combinations for making 7 digits lock is 2,79,936.

What is permutation?

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

Formula for permutation with repetition:

[tex]nP_{r} =n^{r}[/tex]

Where,

P is the total number of combinations.

n is the total number of items in a set

r is the total number of items to be selected from the set

According to the given question.

We have to form a lock that has 7 digits by using numbers from 0 to 5.

⇒ Total numbers of items in a set = 6

and total number of items to be selected = 7

Since, we have to form a lock of 7digits but we have only 6 digits. So we have to repeat this numbers so that we can form a 7 digit lock.

Therefore, the total number of combinations for making 7 digits lock is given by

[tex]6P_{7} = 6^{7}[/tex]

⇒[tex]6^{7}=2,79,936[/tex]

Hence, the total number of  distinct combinations for making 7 digits lock is 2,79,936.

Find out more information about combination and permutation here:

https://brainly.com/question/13387529

#SPJ2

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