An important travel agency collects information about the travel packages they sold. The table below reports the length (in days) of the packages bought by agency's customers. Package length (days) number of packages 4 15 28 6. 43 7 89 8 17 (a) Describe the data: What kind of variable are we dealing with? What are the units? How many units are present in the dataset? (b) Determine relative and cumulative relative frequencies. (c) Packages of more than 6 days are more profitable for the agency. What is the percentage of such profitable packages?

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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.