Water glasses on a shelf are broken and must be replaced. The replacement cost can be cut in half if you can figure out how many glasses were broken. The clues are: There were more than 24 glasses, but less than 100 glasses. If the glasses were in rows of 6, there would be 3 leftovers. If the glasses were in rows of 8, there would be 7 leftovers.
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.
Water glasses on a shelf are broken and must be replaced. The replacement cost can be cut in half if
you can figure out how many glasses were broken. The clues are:
There were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 leftovers.
If the glasses were in rows of 8, there would be 7 leftovers.
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