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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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- Allan Company tracks 8 primary quality characteristics during production of a particular type of coffee maker (the characteristics in this case are ‘opportunities’ that represent the number of critical features that must be correct and therefore represent potential sources of mistakes or errors). After a review of 370 random coffee makers, a team of inspectors finds a total of 22 mistakes. Let each coffee maker represent one “unit”. Notice that on average, the number of mistakes per coffee maker would be 22/370 = 0.0595 dpu. On average, how many mistakes are there per opportunity (i.e., “dpo”)? Use 3 decimal places.A group of researchers at a Department of Sports and Medicine are trying to select the best diet for their athletes. After an extensive literature review, they decide to test three different diets over a period of nine months. Specifically, a sample of 75 athletes are separated into three diet groups (Atkins, Zone and Ketogenic) and their weight is measured at three time points (3 months, 6 months and 9 months). The attached excel sheet presents the data they collected during the study. Here, the numbers in each cell indicate the amount of weight lost (in kilograms) at each time point. What can you conclude from the results of this experiment? *In this question you will find that Levene's test for homogeneity of variance is violated for one of the conditions. You can ignore this continue with the appropriate parametric test. Could you please: Identify the appropriate statistical test. Conduct the statistical test in JASP, Excel or SPSS. Report the complete results (including…A researcher wonders if there an association between the incidence of colds and the amount of vitamin C taken. He recruits 98 volunteers and randomly assigns 29 of them to take 500 mg of vitamin C, 17 of them to take 1000 mg of vitamin C and the rest to take no vitamin C. At the end of the study, it was determined that 28 of the volunteers did not have any colds where 12 of them were in the 500 mg group and 8 of them were in the 1000 mg group. Test the appropriate hypothesis at α=.01 Complete the table of expected counts under the null hypothesis. At least one cold No colds No vitamin C 14.857 500 mg vitamin C 20.714 1000 mg vitamin C 12.143 4.857