Use the Fundamental Counting Principle to solve:A television programmer is arranging the order that five movies will be seen between the hours of 6 p.m. and 4 a.m. Two of the movies have a G rating and they are to be shown in the first two time blocks. One of the movies is rated NC-17 and it is to be shown in the last of the time blocks, from 2 a.m. until 4 a.m. Given these restrictions, in how many ways can the five movies be arranged during the indicated time blocks?
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.
Use the Fundamental Counting Principle to solve:A television programmer is arranging the order that five movies will be seen between the hours of 6 p.m. and 4 a.m. Two of the movies have a G rating and they are to be shown in the first two time blocks. One of the movies is rated NC-17 and it is to be shown in the last of the time blocks, from 2 a.m. until 4 a.m. Given these restrictions, in how many ways can the five movies be arranged during the indicated time blocks?
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