$5.$ I bought a bicycle lock with a six$-$digit code, where each digit was an integer from the set $\{0,1,2,...,9\}.$ The lock came with a card that listed a $$magic$$ code that unlocked the lock. That $$magic code$$ did not repeat any digits.

$($a$)$ How many potential codes are there $($assuming that order matters$).$ Briefly explain.

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ECON $2110$ Problem Set $1$ due June $9,2024$

$($b$)$ Now suppose that if the six digits of the magic code are entered in any order the lockbox will unlock. How many such six$-$digit codes are there? Briefly explain.

$($c$)$ Still assuming that the order of the digits in the code does not matter, how many$-$six digit codes are there that would not unlock the box? Briefly explain.

$($d$)$ What is the probability that a ne$$er$-$do$-$well who knows that the code is six dig$-$ its long $($without replacement$)$ could at random enter the correct code? Explain briefly.