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

A standard deck of cards contains 4 suits (Hearts, Diamonds,
Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7,
8, 9, 10, Jack, Queen, King) for a total of 52 cards.
In a typical game of poker, you are dealt five cards (without
replacement) from a deck of 52 cards. How many Full Houses are
possible?
(A full house is a hand consisting of three of one rank and two
of another. For instance, three...

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I was wondering - how many different possible ways can you make
groups of 3 if you have 15 people in total? It's important to note
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together. Thanks a bunch!

1.A standard poker deck has 52 cards, in four suits (clubs,
diamonds, hears, spades) of thirteen denomination each (2, 3, ...,
10, Jack, Queen, King, Ace, in ascending order). A poker hand
consists of 5 unordered cards. a. How many different poker hands
are possible? (1 point)
b. When drawing 5 cards at random from a poker deck, what is the
probability of drawing two Hearts and a three Spades? (1 point)
2. Five students are to be sampled from...

(a) If 25 women compete in the marathon at the Olympics, in how
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(b) If a three person committee is chosen at random from a group
of 24 people, how many different committees are possible?
(c) in a new lottery game called "Minibucks", you select four
numbers between 1 and 15. If you match all four numbers with the
four numbers chosen by the lottery that day, you...

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