In a middle school class, there are 7 students. A) In how many ways can all 7 students be arranged in a row for a photo? B) From 7 students, how many ways can the teacher selects 3 students for a committee? C)The teacher wants to select 3 students from this class. The first selected student will be a Media Helper, the second one will be a Pledge/Flag Helper, and the third one will be a Pencil Sharpener. From 7 students, how many different ways can this selection be done?
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.
In a middle school class, there are 7 students.
A) In how many ways can all 7 students be arranged in a row for a photo?
B) From 7 students, how many ways can the teacher selects 3 students for a committee?
C)The teacher wants to select 3 students from this class. The first selected student will be a Media Helper, the second one will be a Pledge/Flag Helper, and the third one will be a Pencil Sharpener. From 7 students, how many different ways can this selection be done?
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