5. a) A 4-sided die with numbers 1,2,3,4 on the faces, is rolled n times in row, and the numbers that appear are recorded as a list. Count the lists, where each number appears at least once. b) Consider the set S = {3,7,11,15,19, ...,95,99,103}. At least how many elements must be selected from S to guarantee that there will be at least one pair of numbers in the selection whose sum is 110? Fully explain your answer.
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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