Question

Please show your work and provide explanation!

1a) How many different ways can 40 people be divided into two groups, with at least one person in each group? For example, a partition can be {1} and {2-49}. Another example of a partition could be {1-20} and {21-40}. There is no limit to how many people can be in each group as long as they each have at least one person.

1b) A deck of cards has 52 cards, 4 suits (aces, clubs, diamonds, hearts) with 13 cards (A,2,3,4,5,6,7,8,9,10,J,Q,K} in each suit. How many total ways can you select 4 cards where you have two pairs of two different types of cards? For example, 2 "Queens" and 2 "Eights." Another example, would be 2 "Nines" and 2 "Fours." The order that the cards are selected doesn't matter. However, once a card is selected, it is not replaced.

Answer 1