Suppose two dice (one red, one green) are rolled. Consider the following events: A: the red die shows 3; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 11. Express the given event in symbolic form. The red die shows 3, but the numbers do not add to 11. Au D' A'uD An D' AnD A'n D How many elements does it contain?
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.
![**Scenario: Rolling Two Dice**
When rolling two dice, one red, and one green, consider the following events:
- **Event A:** The red die shows a 3.
- **Event B:** The sum of the numbers on both dice is 5.
- **Event C:** At least one of the dice shows a 1.
- **Event D:** The sum of the numbers on both dice does not add up to 11.
**Task**
Express the following situation in symbolic form:
"The red die shows 3, but the numbers do not add to 11."
**Symbolic Representation Options:**
- \( A \cup D' \)
- \( A' \cup D \)
- \( A \cap D' \)
- \( A \cap D \)
- \( A' \cap D \)
The correct symbolic form is: \( A \cap D \).
**Question**
How many elements does this event contain?
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