26) Seven cards cachcotaining one of the letters in the word "AIABAMA are placed in a box. If one card is chosen at random, what is the probability that the card chosen will be an A?
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.
![### Probability Question on Letter Selection
#### Question 26:
Seven cards, each containing one of the letters in the word "ALABAMA," are placed in a box. If one card is chosen at random, what is the probability that the card chosen will be an A?
**Options:**
A) \( \frac{1}{7} \)
B) 7
C) \( \frac{2}{3} \)
D) \( \frac{1}{2} \)
#### Explanation:
To solve this probability question, we need to determine the number of favorable outcomes and the total number of possible outcomes.
- **Total Number of Cards:** 7 (since there are 7 letters in "ALABAMA")
- **Number of A's in the word "ALABAMA":** 4
The probability \( P \) of selecting an 'A' is given by the formula:
\[ P(\text{'A'}) = \frac{\text{Number of 'A's}}{\text{Total Number of Cards}} \]
Substituting the values:
\[ P(\text{'A'}) = \frac{4}{7} \]
Therefore, the correct answer is not provided in the options given. The understanding of the problem and the approach to solve it is important despite the error in the given choices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f5b0c2e-6059-4e7d-9b71-cff7feb80651%2F746f70d3-9a53-4c19-9cd6-2e36b080aadd%2Fsvixf57_processed.jpeg&w=3840&q=75)
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