In: Advanced Math
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 and setting up appropriate subsets 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...)