Assume that you have 4 dimes and 5 quarters (all distinct), and you select 3 coins. (1) In how many ways can the selection be made? (2) In how many ways can the selection be made if all the coins are dimes? (3) In how many ways can the selection be made if you select 2 dimes and 1 quarter? (4) In how many ways can the selection be made so that at least 2 coins are dimes?
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.
Rework problem 9 from section 2.3 of your text. Assume that you have 4 dimes and 5 quarters (all distinct), and you select 3 coins.
(1) In how many ways can the selection be made?
(2) In how many ways can the selection be made if all the coins are dimes?
(3) In how many ways can the selection be made if you select 2 dimes and 1 quarter?
(4) In how many ways can the selection be made so that at least 2 coins are dimes?
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