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How many 10 letter words can you make from the letters A,B,C,D,E,F,G and H?

Question

How many 10 letter words can you make from the letters A,B,C,D,E,F,G and H?

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Solution

To determine how many 10-letter words can be made from the letters A, B, C, D, E, F, G, and H, we need to consider the following:

  1. Number of letters available: We have 8 distinct letters (A, B, C, D, E, F, G, H).
  2. Length of the word: We need to form a 10-letter word.

Since we are allowed to use each letter more than once, this is a problem of permutations with repetition.

For each of the 10 positions in the word, we have 8 choices (one for each letter).

Therefore, the total number of 10-letter words is calculated as: 810 8^{10}

Now, let's compute this:

810=8×8×8×8×8×8×8×8×8×8 8^{10} = 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8

810=1073741824 8^{10} = 1073741824

So, the number of 10-letter words that can be made from the letters A, B, C, D, E, F, G, and H is 1,073,741,824.

This problem has been solved

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