1.) Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 15 movies during the year, how many ways can the three best be chosen and ranked? Show your work in the space provided.
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.
1.) Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 15 movies during the year, how many ways can the three best be chosen and ranked?
Show your work in the space provided.
2.) To win the Florida lottery, one must correctly select 5 numbers from 58 numbers. The order in which the selection is made does not matter. How many different selections are possible?
Show your work in the space provided.
3.) Baskin-Robbins offers 31 different flavors of ice cream. One of their items is a bowl consisting of 4 scoops of ice cream, each a different flavor. How many such bowls are possible?
Show your work in the space provided.
4.) For a radio segment at a local station, a disc jockey can play 6 records. If there are 12 records to select from, in how many ways can the program for this segment be arranged?
Show your work in the space provided.
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