Oliver (cat) and Dodger (dog) belong to a club of cats and dogs. There are five dogs and six cats in the club. For each case below: how many ways can a committee of four be selected to work on finding food next Saturday? a) There must be two dogs and two cats. b) There must be at least two cats. c) Oliver and Dodger must be on the committee. d) There must be more dogs than cats.
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.
Oliver (cat) and Dodger (dog) belong to a club of cats and dogs. There are five dogs and six cats in the club. For each case below: how many ways can a committee of four be selected to work on finding food next Saturday?
a) There must be two dogs and two cats.
b) There must be at least two cats.
c) Oliver and Dodger must be on the committee.
d) There must be more dogs than cats.
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