1. Expand (x + y)8 using binomial theorem?

2. In the movie \Cheaper by the Dozen," there are 12 children in the family.

(a) Prove that at least two of the children were born on the same day of the week;

(b) Prove that at least two family members (including mother and father) are born in the same month;

(c) Assuming there are 4 children's bedrooms in the house, show that there are at least 3 children sleeping in at least one of them.

3.You have one standard 6-sided die. You roll it 3 times and record the results.

a)How many possible outcomes are there?

b)What is the probability that you get all 6s ?

c)What is the probability that you get exactly two 6s?

COURSE CODE IS 362 combinatorial analysis

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