The local nows station wants to interview 8 students from a school. There are 25 students on he Studar aduating class and 15 are from the other classes. The principal has a difficult time deciiing which students from the council will get intorviewed, so she s the group of students that she will put all of the names in a bow, mix the names, then tho first 8 rames who are seleated from the bowl wil got to te Interviewed. a next day, the principal returno vwith the names sclected. I turns out that 5 of the students who got to be interviowed are in the graduating claas and only of the students seloctod are from othor classes. The siudents who are not in the graduating class cormplain that this doesn't soern fair. They suspHct that the principal chose the group rather than selecting at random. Do you think the principal could have choson this group of students at random lke she promised? Explain your
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.
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Unit 4. Lesson 8: Not Always Ideal
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Is that Fair?
Tho local news station wants to interview 8 students from a school. There are 25 students on the student council. Ten of the students are from the
raduating class and 15 are from the other classes. The principal has a difficult time deciding which students from the council will get interviewed, so she
ells the group of students that she will put all of the names in a bowl, mix the names, then the first 8 rames who are selected from the bowl wil get to bbe
interviewed.
ne next day, the principal returms with the names sclected. It turns out that 5 of tne students who get to be interviowed are in the graduating ciass and only
3 of the students selected are from other classes. The studonts who are not in the graduating class complain that this doesn't seern fair. They suspHct that
the principal chose the group rather than selecting at randorm.
Do you think the principal could have choson this group
of students at random lke she promised? Explain your
reasoning.
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