Cash prizes are given out to the top 3 performers. First place wins $200. Second place wins $100. Third place wins $50. How many different possible ways are there to give out the 3 prizes if each student is allowed to win no more than one prize? b) In addition, 4 of the 12 competitors are randomly selected to win a subscription to the Mathematical Weekly journal. How many different groups of 4 winners may be selected from the 12 contestants?
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.
There are 12 students in a math league competition.
(
a) Cash prizes are given out to the top 3 performers. First place wins $200. Second place wins $100. Third place wins $50. How many different possible ways are there to give out the 3 prizes if each student is allowed to win no more than one prize?
b) In addition, 4 of the 12 competitors are randomly selected to win a subscription to the Mathematical
Weekly journal. How many different groups of 4 winners may be selected from the 12 contestants?
Step by step
Solved in 2 steps
