Distance to School (in minutes) School Student 1 2 3 5 6 Amy 15 30 60 30 45 20 Brent 10 30 45 20 45 10 Calvin 30 45 20 60 20 30 Deidre 20 30 45 15 10 45 Elena 45 20 15 45 15 30 Franklin 15 45 30 15 20 60
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.
Assign students to schools such that travel time is
minimized.
![Distance to School (in minutes)
School
Student
1
2
3
5
6
Amy
15
30
60
30
45
20
Brent
10
30
45
20
45
10
Calvin
30
45
20
60
20
30
Deidre
20
30
45
15
10
45
Elena
45
20
15
45
15
30
Franklin
15
45
30
15
20
60](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faec88732-33c2-4c2e-a388-68558acd3a45%2Fa4362db3-68f1-4c8a-af53-7e3971617d17%2Fgzx3bn_processed.png&w=3840&q=75)
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