The different sequences that are there on the dial without repeating a number are 19656.
We have a 3 digit sequence to open the lock of padlock of the locker. The 3 digits are in range between 1 and 28.
We have to find how many different possible sequences that can be used for the padlock without repeating the digit.
A permutation is a method that is used to estimate the number of possible arrangements of the given values, considering the order of arrangement of the values.
We can use the mathematical formula of permutation to solve the problem given to us.
The total no of possible arrangements can be calculated using the formula -
[tex]\frac{n!}{(n-r)!}[/tex]
In our case : n = 28 and r =3, substituting the values we get -
[tex]\frac{28!}{(28-3)!} \\\\\frac{28!}{25!} \\\\\frac{(28)(27)(26) (25!)}{25!} \\\\\\[/tex]
[tex]28[/tex] x [tex]27[/tex] x [tex]26[/tex] = 19656
Hence, the different sequences that are there on the dial without repeating a number are 19656.
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