A teacher is decorating their classroom by placing posters in a row on one wall. The teacher has 7 posters , of which 4 are colored and 3 are black & white. a) If the teacher decides to only use 5 posters, how many arrangements can be made? Show how to get your answer using two different methods. b) If the teacher uses all 7 posters, but wants to have a black & white poster at each end, how many arrangements can be made ?
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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