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