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What is the total number of different -letter arrangements that can be formed using the letters in the word HYPOTENUSE?Answer:
Full solution
Q. What is the total number of different -letter arrangements that can be formed using the letters in the word HYPOTENUSE?Answer:
- Identify Letters Count: Identify the number of each letter in the word HYPOTENUSE.H - , Y - , P - , O - , T - , E - , N - , U - , S -
- Calculate Factorial: Calculate the factorial of the number of letters in the word. Since there are letters in the word HYPOTENUSE, we calculate ( factorial).
- Adjust for Repeated Letters: Adjust for the repeated letters. Since the letter 'E' appears twice, we need to divide the total by the factorial of the number of times 'E' appears to correct for overcounting.We divide by because 'E' appears twice.
- Calculate Final Arrangements: Calculate the final number of arrangements by dividing the total number of arrangements by the number of repeated letter arrangements.Number of arrangements = Number of arrangements =
