There are several ways the door can be locked, these ways illustrate combination.
There are 3375 possible combinations
From the question, we have:
--- the number of digits
---- the number of actions
Each of the three actions can either be:
- <em>Pressing one button</em>
- <em>Pressing a pair of buttons</em>
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The number of ways of pressing a button is:
Apply combination formula
The number of ways of pressing a pair is:
Apply combination formula
So, the number of ways of performing one action is:
For the three actions, the number of ways is:
Hence, there are 3375 possible combinations
Read more about permutation and combination at: