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The problem is asking how many permutations of the letters "ABCDEFG" contain the string "BCD."

### Step-by-step solution:

- The word consists of 7 distinct letters: A, B, C, D, E, F, G.
- However, we are told that the string "BCD" must be treated as a single unit or "block." So instead of considering B, C, and D as individual letters, we treat them as a single block.
  
Thus, instead of 7 letters, we now have 5 units to arrange:
1. The block "BCD"
2. A
3. E
4. F
5. G

### Permutations:
Since there are 5 units to arrange, the number of permutations is simply \( 5! \) (5 factorial):

\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]

Therefore, **the number of permutations that contain the string "BCD" is 120**.

Would you like more details on this, or do you have any questions?

Here are some related questions to explore this topic further:

1. How would the answer change if the letters B, C, and D could appear in any order?
2. What if the string required was "BDF" instead of "BCD"?
3. How many total permutations are there of the letters "ABCDEFG" without any restrictions?
4. What if the string "BCD" could appear in reverse order as well, like "DCB"?
5. How would you calculate permutations if some letters were repeated, instead of all being distinct?

**Tip:** When solving permutation problems with blocks of fixed positions, always reduce the total number of elements based on the blocks and calculate the factorial of the remaining elements.

How many permutations of the letters ABCDEFG contain the string BCD?

Explore how many permutations of the letters ABCDEFG contain the string BCD. This problem involves key concepts from combinatorics and permutations, with a step-by-step breakdown using the factorial formula. Suitable for Grades 9-12.

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