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If we are asked how many 5 digit lock codes we can make, are we dealing with permutations or combinations?

User Rithik
by
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1 Answer

4 votes

Answer:

Permutations

Explanation:

We are dealing with permutations because the order of the digits matters. For example, 12345 and 54321 are different lock codes.

Here's why:

  • Permutations: The order of the items matters.
  • Combinations: The order of the items does not matter.

In the case of a 5-digit lock code, the order of the digits matters because each digit represents a different position on the lock. If we enter the digits in the wrong order, the lock will not open.

To calculate the number of possible permutations for a 5-digit lock code, we can use the following formula:


\sf (n!)/((n-r)!)

where:

n is the total number of items (in this case, 10 digits)

r is the number of items we are selecting (in this case, 5 digits)

So, the number of possible permutations for a 5-digit lock code is:


\sf (10! )/( (10-5)! )=(10!)/(6!) =(10* 9* 8* 7* 6!)/(6!)= 30,240

This means that there are 30,240 possible lock codes for a 5-digit lock.

User Gluecksmelodie
by
7.3k points
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