6. Seven cross country runners will be chosen from the SFSU cross country team of 14 to represent the team at a fundraiser. (a) How many different groups of seven are there? (b) If three out of seven cross country runners have a chance to rank first, second, and third place. How many ways can three of the seven players rank in first, second, and third place?
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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