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EE380 Project 2 Binomial Coefficient

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Question 1)
A certain population consists of N=1000 people. 500 of them support party A; 300 of them
support party B; and 200 support party C. A group of 4 people is chosen at random from the
population. What is the probability that all persons in the group support
a) party A
b) party B
c) party C

Question 2)
A class of 4n children contains 2n boys and 2n girl. A group of 2n children is chosen at random.
What is the probability that the group contains an equal number of boys and girls?
For:
a) n=10
b) n=50

Question 3)
In a lottery game, the player picks 4 numbers from a sequence of 1 through 20. At lottery
drawing, 4 balls are drawn at random from a box containing 20 balls numbered 1 through 20.
What is the probability that the player will win the lottery (i.e. getting 4 matches in any order)?