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Combinations

1. The coefficient of x^7y^2 in the expansion of (2x-y)^9

2. How many subsets of {2,3,5,7,11, 13, 17,19,23) contain four numbers?

3. If a committee varies its meeting days, how many meetings must it schedule before we can guarantee that at least two meetings will be held on the same day of the week??

4. How many different 4 -person delegations can be found from a group of 12 people??

5. In how many different ways can 10 quarters be distributed to 5 people?

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1. The coefficient of x^7y^2 in the expansion of (2x-y)^9

Solution. By the binomial formula, we know that the coefficient of x^7y^2 in the expansion of (2x-y)^9 is
4608

2. How many subsets of {2,3,5,7,11, 13, 17,19,23) contain four numbers? ...

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Combinations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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