Question

# 1.A standard poker deck has 52 cards, in four suits (clubs, diamonds, hears, spades) of thirteen...

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)

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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