The minimum number of words in set A that must begin with the same alphabet is 27, as each word starts with a unique letter from the English alphabet.
The number of possible passwords can be determined by considering the requirements given. Each password must contain at least one digit and must start with a letter.
Let's break down the calculation step-by-step:
1. For the first character, there are 26 possible choices (all uppercase letters).
2. For the remaining characters, there are 36 possible choices (26 uppercase letters + 10 digits).
3. Since there are no restrictions on the length of the password, we can choose any number of characters after the first one.
To calculate the total number of possible passwords, we multiply the choices for each character together. So the formula would be:
26 (choices for the first character) * 36^n (choices for the remaining n characters)
where n represents the number of characters after the first one.
Let's consider an example. If we have a password with 4 characters after the first one, the calculation would be:
26 * 36^4 = 26 * 36 * 36 * 36 * 36 = 26 * 1,679,616 = 43,654,016 possible passwords.
Therefore, the number of possible passwords depends on the number of characters after the first one, with each additional character significantly increasing the number of possibilities.
For the second question, we are asked to determine the minimum number of words in set A that must begin with the same alphabet. To find the answer, we need to consider the number of distinct English words in set A.
Given that there are 27 distinct English words in set A, we can assume that each word starts with a different alphabet letter. Therefore, the minimum number of words in set A that must begin with the same alphabet would be at least 27, as each word starts with a unique letter.
To further clarify, if we have a set A with the following words:
apple, banana, cat, dog, elephant, ...
Each word begins with a different alphabet letter, so the minimum number of words that must begin with the same alphabet is 27.In conclusion, the minimum number of words in set A that must begin with the same alphabet is 27, as each word starts with a unique letter from the English alphabet.
Learn more about possibilities here,