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.
![### Question 5: Pythagorean Theorem Application
**Problem Statement:**
Find the value of \( a \) in the triangle. Approximate the value to three decimal places.
**Triangle Description:**
- It is a right-angled triangle.
- One leg measures 30 units.
- The other leg measures 23 units.
- The hypotenuse is denoted as \( a \).
**Solution Choices:**
- A. 37.802
- B. 19.261
- C. 7.280
- D. 19
**Diagram:**
This problem includes a right triangle diagram with:
- A right angle marked at one vertex.
- The vertical leg is labeled as 30.
- The horizontal leg is labeled as 23.
- The hypotenuse is labeled \( a \).
### Explanation:
To find the value of \( a \) (the hypotenuse) in a right-angled triangle, the Pythagorean theorem is used:
\[ a^2 = 30^2 + 23^2 \]
Calculating the squares:
\[ 30^2 = 900 \]
\[ 23^2 = 529 \]
Adding these values:
\[ 900 + 529 = 1429 \]
Taking the square root of the sum to find \( a \):
\[ a = \sqrt{1429} \approx 37.802 \]
Thus, the correct answer is:
\[ A. 37.802 \]
### Conclusion
- **Correct Answer:** A. 37.802](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6756c5c2-608f-4015-b13f-deb910f8c3e1%2Ff9a5e32c-9b09-4bfb-bc2e-357abb33ebe6%2Fqe6n6qn_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
