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.
![### Geometry Problem on Angles
Below is a diagram featuring a geometric figure consisting of points A, B, C, and D connected by lines. The points are labeled as follows:
- A, C, and B are collinear.
- D is a point that creates angle ACD with line segment AC and angle DCB with line segment CB.
### Diagram:
```
D
•
/
/
A •-----• C -----• B
```
### Given Information:
1. The measure of angle ACB is 180° (indicating a straight line).
2. The measure of angle ACD is 55°.
### Problem Statement:
If the measure of angle ACB (angle ∠ACB) is 180°, and the measure of angle ∠ACD is 55°, then what is the measure of angle ∠DCB?
\[ m\angle ACB = 180^\circ \]
\[ m\angle ACD = 55^\circ \]
What is \( m\angle DCB = [ ? ]^\circ \)
To submit your answer, please use the form below:
[ ] \( \text{Enter degrees} \)
```
[Enter]
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64142f79-a87a-4aef-a78d-f40a1d13dd04%2Fbc885384-bff0-4c9f-910e-15e660035757%2Frmykabd_processed.jpeg&w=3840&q=75)
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