## Locker Combinations and Permutations

### Topic

Locker Combinations and Permutations

### Vocabulary

- Permutation
- Combination

### Student Exploration

#### How many different locker combos can a combination lock have?

It is Fall and school is back in session, Denise needs to buy a lock for her school locker. She wants her belongings to be safe, but she doesn’t want to carry around a key and would rather have a lock with a combination. Before going shopping she decides to research locks online and wants the deciding factor to be the number of locker combination codes that the lock has, that way a thief will have a nearly impossible task of breaking her lock’s combination code.

Research different locks online and find three different models with different designs and set-ups for the locker combos. Then determine which one you would recommend to Denise as the safest for protecting her belongings, using your math work as evidence!

### Extension Investigation

One of the locks Denise considers is a circular lock with 20 numbers. To open it she turns the dial to the first number, then she turns the dial to the second number, and then she turns it to the third number. She may not repeat numbers in her locker combo.

a. Why does this situation represent a Permutation?

b. Write an expression for the number of different combination codes that are possible with this lock?

c. If Denise could use four numbers in her locker combo, how would you approach this task?

d. If Denise could repeat numbers in her locker combo, how would you approach this task?

e. If Denise could choose from 40 different number, rather than 20, how would you approach this task?

f. What would need to change in the problem in order for it to represent a Combination?

g. Why doesn’t it make sense for locks to be “Combination Locks”?

### Connections to other CK-12 Subject Areas

- Combination Problems
- Permutations and Combinations Compared
- Permutations with Repetition