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.
![The image contains a mathematical expression, written vertically, which is part of a question or problem labeled "f)". The expression is:
\[ (3 \leq x - 4 \leq 3) \cup \{x \mid x \leq 3\} \]
This consists of two parts:
1. A compound inequality:
\[ 3 \leq x - 4 \leq 3 \]
This inequality suggests that \( x - 4 \) is bounded between 3 and 3.
2. A set notation expression:
\[ \{x \mid x \leq 3\} \]
This represents the set of all \( x \) such that \( x \) is less than or equal to 3.
3. A union symbol ( \( \cup \) ) connecting the two expressions, indicating that the solution is the union of the two sets derived from each part.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028128fd-b27f-44d7-985e-59cd58409734%2F51244fc7-5912-4d4d-bdbc-9157b292c47c%2Fuzj2v7s_processed.jpeg&w=3840&q=75)
Given information:
where The symbol '|' placed between 2 x's stands for such that.
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