Solve the problem.

How many different 6-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed.
Group of answer choices

1,771,561

720

332,640

462

To solve the problem, we need to find the number of different 6-letter sequences that can be made using the first 11 letters of the alphabet (A, B, C, D, E, F, G, H, I, J, K) with repetition of letters allowed.

Since repetition is allowed, each position in the sequence can be filled with any of the 11 letters.

Therefore, the total number of possible sequences is calculated as:

\[
11 \times 11 \times 11 \times 11 \times 11 \times 11 = 11^6
\]

Now, let's calculate \(11^6\).

\[
11^6 = 1771561
\]

So, the correct answer is:

\[
\boxed{1,771,561}
\]

Do you want details or have any questions? Here are some related questions to deepen your understanding:

1. How many different 4-letter sequences can be made using the first 10 letters of the alphabet?
2. What is the probability of randomly selecting a sequence that starts with 'A'?
3. How would the answer change if repetition of letters was not allowed?
4. How many different 5-letter sequences can be made using all 26 letters of the alphabet?
5. What is the number of different sequences if only 8 letters of the alphabet are used?

**Tip:** When repetition is allowed, the formula to calculate the number of sequences is the base (number of available options) raised to the power of the sequence length.

Discover how many different 6-letter sequences can be made using the first 11 letters of the alphabet with repetition allowed. Learn the formula and calculation method for permutations with repetition. Suitable for students in Grades 7-9.

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