The UCLA Math Team gives out 3 different awards to graduating students who were active on the team. This year, there are 10 graduating students who were active on the team. a) How many different ways are there to give out the 3 awards if students are allowed to win more than one award? b) How many different ways are there to give out the 3 awards if each student is allowed to win no more than one award? c) At the end of year math party, 4 students are randomly selected and each student wins a calculator. How many different groups of 4 winners may be selected from the 10 team members?
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.
The UCLA Math Team gives out 3 different awards to graduating students who were active on the team. This year, there are 10 graduating students who were active on the team.
a) How many different ways are there to give out the 3 awards if students are allowed to win more than one award?
b) How many different ways are there to give out the 3 awards if each student is allowed to win no more than one award?
c) At the end of year math party, 4 students are randomly selected and each student wins a calculator. How many different groups of 4 winners may be selected from the 10 team members?
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