Finding Binomial Coefficients and Combinations
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Committees of 5 individuals are to be formed from 8.
a) How many committees are there?
b) How many committees of 5 can be formed from 8, given that two particular individuals are to be included on the committee?
c) How many committees of 5 can be formed from 8, given that two particular individuals are to be excluded from the committee?
d) How many committees of 5 can be formed from 8, given that at least one of two particular individuals is to be on the committee?
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Solution Summary
This solution shows how to determine the number of ways to pick the committees in an attached Word document.
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See attached
Solution.
a) If there are no restrictions, then we can choose 5 people from the given 8 people. The total number of possible ways is 56 (See attached for calculations)
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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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