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.
![### Segment Lengths in Geometry
#### Find the Length of Segment CD
Below is a diagram showing several points on a line segment:
```
A -------- B -------- C -------- D -------- E
```
Given the following segment lengths:
- CE = 8
- AB = 5.5
- AD = 15.5
- AE = 18.5
We are tasked with finding the length of segment CD.
**Known values:**
- CE (the segment from point C to point E) is 8 units.
- AB (the segment from point A to point B) is 5.5 units.
- AD (the segment from point A to point D) is 15.5 units.
- AE (the segment from point A to point E) is 18.5 units.
To find the length of CD (the segment from point C to point D), you need to consider the segment lengths provided.
The following equation can help solve for CD:
\[ AE = AD - CD - CE + AB \]
**Simplifying equations:**
\[
AE - AD = CD + CE - AB \\
18.5 - 15.5 = CD + 8 - 5.5 \\
3 = CD + 2.5 \\
CD = 3 - 2.5 \\
CD = 0.5
\]
**Derived value:**
- CD = 0.5 units
Please verify all calculations and confirm the result using geometric context and logical deduction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc0a5f26-bbf4-4ae4-8d89-37ec0e55f729%2Fb60fd7f7-6d32-4ada-bbaf-1637b65228b9%2F2oo60u7_processed.jpeg&w=3840&q=75)
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