$-$if all three numbers in

the code must be different

$($something like $9-9-9$ is not

allowed$),$ how many codes

are possible?

$-$if duplicated numbers are

allowed in the code $($some$-$

thing like $9-9-9$ is allowed$),$

how many such codes are

possible?

$-$if duplicated numbers are

possible, but consecutive

entries in the code must be

different $($something like $9-$

$8-9$ is allowed, but $9-9-9,9-$

$9-8,$ and $9-8-8$ are not$),$ how

many codes are possible?

The dial on the lock shown allows

for non$-$negative integer values

$0$ through $39.$ Locks like this

typically have a three$-$number

code.

$-$Does the lock's code fit the

mathematical definition of a

combination? Or is it better

described as a permutation?

Explain