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12-49.

Joaquin is getting a new locker at school and the first thing he must do is decide on a new combination. The three‑number locker combination can be selected from the numbers $0$ through $21$. 12-49 HW eTool (Desmos).

1. How many different locker combinations can Joaquin choose if none of the numbers can be repeated?

In this case the common use of the word “combination” conflicts with the mathematical meaning.

2. With your understanding of permutations, combinations, and factorials, decide if the name “combination lock” is appropriate.

3. How many mathematical combinations are possible?

$_{22}C_3=1540$, but this doesn't make sense for a mechanical lock because it implies dialing the numbers in any order to open the lock.

4. How many choices would there be if you could repeat a number, but not use the same number twice in a row?

$22·21·21 = 9702$

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