How many ways can 120 identical packages be loaded into 10 delivery trucks where some trucks may have no packages? The delivery truck driver union is concerned that the workload is unequal. How many ways can 120 identical packages be loaded into 10 delivery trucks where each truck must have at least 5 packages? How many ways can 120 unique packages be loaded into 10 delivery trucks where each truck must have the same number of packages?
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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