A deck of 52 cards is shuffled and divided into two stacks of 26 cards. If you repeat this process 2000 times, each time checking the contents of each pile, how many times could you expect the number of red cards in one pile to match the number of black cards in the other?
What is the number of ways of choosing 4 cards from a deck of 52, where all the cards are of the same suit and secondly, where all the cards are of different suits?