Sequences If 11 people run a race, how many sequences of 1st, 2nd, 3rd, and 4th place winners can there be? Express your answer as a fraction of integers, but only use foctorials of integers for the numerator and denominator. For example, if the denominator is 23!4!, then enter 23!4! with no mulitplication symbol and no spaces. The numerator is and the denominator is When this fraction is converted by calculation to a single integer, that integer is:
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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