The security manager for a large company, Mr Hugh Jintellect, was giving a presentation to the board regarding the new security arrangements for the building. “There will be a panel on each doorway with buttons numbered 1 to 5. To gain entry a person will have to enter a code consisting of 5 different digits by pressing the buttons in correct sequence.” Jimbo spoke up and said, “To save time why don’t you make it just 4 out of the 5 numbers?”
Hugh replied, “We feel that reducing the number from 5 to only 4 digits will not provide enough combinations to exclude random guesses.” Why was poor Hugh sacked by the board?
Answer
Hugh was sacked because he did not realise that reducing the number of buttons from 5 to 4 leaves exactly the same number of possible combinations of different buttons.
For 5 buttons the number of combinations is 5x4x3x2x1= 120.
For 4 buttons it is 5x4x3x2 = 120.
After you have chosen 4 different numbers from the 5, there is only one possible fifth number remaining, so it adds no extra choices to the number of combinations.
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