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What is the total number of different -letter arrangements that can be formed using the letters in the word FUNDAMENTAL?Answer:
Full solution
Q. What is the total number of different -letter arrangements that can be formed using the letters in the word FUNDAMENTAL?Answer:
- Count Letters: First, count the number of each letter in FUNDAMENTAL. We got , , , , , , , , , , . Notice that appears twice and appears twice.
- Calculate Formula: Since the word FUNDAMENTAL has letters with Ns and As, the formula for the number of arrangements is .
- Calculate : Calculate which is .
- Calculate : Calculate which is , and since we have two s, it's .
- Divide Factorial: Now divide by the product of the two s. So, it's .
- Perform Division: Perform the division to get the number of arrangements. The calculation is .
- Simplify Result: The result is . Simplify this to get $\(11\) \times \(10\) \times \(9\) \times \(8\) \times \(7\) \times \(6\) \times \(5\) \times \(4\) \times \(3\) \times \(2\) \times \(1\) / \(4\) = \(11\) \times \(10\) \times \(9\) \times \(8\) \times \(7\) \times \(6\) \times \(5\) \times \(4\) \times \(3\) \times \(2\) \times \(1\) / \(4\) = \(11\) \times \(10\) \times \(9\) \times \(8\) \times \(7\) \times \(6\) \times \(5\) \times \(2\) \times \(3\) \times \(2\) \times \(1\).
