A local sandwich shop offers fivedifferent breads, four different meats, three differentcheeses, and six different vegetables. A customer canchoose one bread, one or no meat, one or no cheese,and up to three vegetables. Find the total number ofcombinations of sandwiches possible.
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.
A local sandwich shop offers five
different breads, four different meats, three different
cheeses, and six different vegetables. A customer can
choose one bread, one or no meat, one or no cheese,
and up to three vegetables. Find the total number of
combinations of sandwiches possible.
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