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r-ruslan [8.4K]
3 years ago
11

A locker combination system uses three digits from 0 to 9. How many different three-digit combinations with no digit repeated ar

e possible?
Mathematics
1 answer:
ruslelena [56]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that a locker combination  system uses three digits from 0 to 9.

Repitition is not allowed.

Three digits can start with 0 also.

Here since order matters, permutation should be used.

Hence 3 digits for lock without repitition from 10 digits can be done in 10P3 ways

=10*9*8

=720

There are 720 different combinations

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<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20-22x%3D10%5C%5C" id="TexFormula1" title="x^{2} -22x=10\\" alt="x^{2} -22x=10\\"
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x^2 - 22x = 10

Next step is to complete the square on the left hand side of the equation and it would be balanced by adding the same number to the right side of the equation. It becomes

x^2 - 22x + (22/2)^2 = 10 + (22/2)^2

x^2 - 22x + (11)^2 = 10 + (11)^2

x^2 - 22x + (11)^2 = 10 + 121

x^2 - 22x + (11)^2 = 131

x^2 - 22x + 121^2 = 131

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