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Let n > 5. A deck containing 4n cards has exactly n cards each of four...

Let n > 5. A deck containing 4n cards has exactly n cards each of four diffrent suits numbered from the set [n].

Using the method of choice (or otherwise) in how many ways can five cards be chosen so that they contain:

(a) five consecutive cards of the same suit? (ie. the set of numbers on the cards is [i, i + 4])

(b) four of the five cards have the same number?

(c) exactly three of the cards have the same number?
(d) not more than two cards of the same suit? Hint: consider two cases.

give a justification of answers pls (set notation, bijection principal, addition or multiplication theorem, cartesian product etc...)

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