A pet store surveyed 683 people to see how many own a fish, how many own a cat, and how many own a bird. The Venn diagram below shows the results. (Each number gives the number of people who fall into that Venn diagram category.) All people in the survey (a) How many of the people own exactly one of the three types of animals? Own a fish Own a cat Opeople 125 52 121 (b) How many of the people own a cat? 64 I people 39 124 81 (c) How many of the people own both a bird and a fish, but don't own a cat? 77 Own a bird O people
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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