This is the first question I answer on the subject so I require assistance.
We are asked the following:
In how many different ways can I draw 6 cards out of a deck with 52 cards, such that i drew at least 1 of each shape (hearts, spades, diamonds, clubs).
can anyone give me a hint in the right direction?
I have an idea but it seems very difficult, perhaps there is a better way.
I'm thinking of saying $DD$= set of 4 different shapes + 2 diamonds, $DH$ = set of 4 different shapes + another heart + another diamond,$DS$ 4 of each + another diamond + another spade, etc...find the cardinality of all these sets, and invoke inclusion-exclusion. But that seems very very difficult.