For this problem, assume the cooler contains 28 cans, 10 of which are regular, and the rest of which are diet. (1) How many ways can you choose 5 cans from the cooler? (2) How many ways can you choose 5 regular cans from the cooler? (3) How many ways can you choose 5 diet cans from the cooler?
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.
For this problem, assume the cooler contains 28 cans, 10 of which are regular, and the rest of which are diet.
(1) How many ways can you choose 5 cans from the cooler?
(2) How many ways can you choose 5 regular cans from the cooler?
(3) How many ways can you choose 5 diet cans from the cooler?
(4) How many ways can you choose 5 cans from the cooler so that at least 4 are diet?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
