Question

Combination Lock The typical combination lock uses three numbers, each between 0 and 49. Opening the lock requires entry of the three numbers in the correct order. Is the name “combination” lock appropriate? Why or why not?

Short answer

The name “combination” lock is inappropriate as the code for opening the lock requires the use of permutation, not combination.

Step-by-step solution

Given information

The code for opening a lock comprises three digits to be chosen from 0 to 49.

The order of the digits is important for opening the lock.

Define combination and permutation

Combination: Count the ways to select a specific number of items from a list without replacement inwithout any particular order.

Permutation: Count the ways to select a specific number of items from a list without replacement inwhere orders matter.

Identify the technique to be used

It is given that the code for opening the lock needs three digits to be chosen from 0 to 49.

The arrangement of the digits matters in opening the lock.

The following two cases can appear:

• The digits may repeat (selected with replacement): In this case, neither combination nor permutation can be used. Thus, the name combination lock is inappropriate.
• The digits cannot repeat (selected without replacement): In this case, either combination or permutation can be used. Here, as the order of the digits is important, the technique of permutation would be used. Thus, the name “combination” lock is inappropriate because permutation will be used to open the lock instead of combination.