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Combinations

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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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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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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? ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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