Question: I need help with Discrete Mathematics Please provide a clear explanation and thorough work. If possible please explain your approach as well just so I

I need help with Discrete Mathematics

Please provide a clear explanation and thorough work. If possible please explain your approach as well just so I could understand it better. The more detail the better thank you.

1) Prove that for all positive integers n, that 5^n - 1 is divisible by 4. Please give two different proofs of this, one using induction and one using modular arithmetic.

3) You are making license plates in Alaska, where the plates have the design of three letters followed by three digits. How many possible license plates are there that

a) don't contain the letter p and don't contain the digit 3?

b) don't contain the letter p or don't contain the digit 3?

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