Question

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 class of 30 students to form a committee consisting of a President, a Vice-President, a Secretary, a Treasurer, and a Councilor. In how many different ways can this committee be formed with the students from this class? (1 point)

Answer #1

1. a. Since there are 52 unique cards in a standard poker deck, and we are to choose 5 cards randomly from these 52 cards. The number of possible hands of poker are :

b. Number of possible poker hands with 2 hearts and 3 spades

When drawing 5 cards at random from a poker deck, the probability of drawing two Hearts and three Spades is

= 22308/2598960

= 0.008583433

2. Five students are to be sampled from a class of 30 students to form a committee consisting of a President, a Vice-President, a Secretary, a Treasurer, and a Councilor. This committee can be set up from the students of the class in the following number of ways:

= 30x29x28x27x26

= 17100720

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