Mary wants to buy a new car. The model she likes comes with exterior colors of (in order from darkest to lightest) black, navy, burgundy, green, tan, and white. Interior colors have the same options, but the interior must be the same as, or lighter than, the exterior color, with the exception that no cars combine green with burgundy or green with navy. Hood ornaments may be ordered for cars that are burgundy (inside, outside, or both). Sunroofs may be ordered for cars with white or tan interiors. Fancy hubcaps are available for cars with black or navy exteriors. How many different styles of cars are available?
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.
Mary wants to buy a new car. The model she likes comes with exterior colors of (in order from darkest to lightest) black, navy, burgundy, green, tan, and white. Interior colors have the same options, but the interior must be the same as, or lighter than, the exterior color, with the exception that no cars combine green with burgundy or green with navy. Hood ornaments may be ordered for cars that are burgundy (inside, outside, or both). Sunroofs may be ordered for cars with white or tan interiors. Fancy hubcaps are available for cars with black or navy exteriors. How many different styles of cars are available?
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