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What is the total number of different 10-letter arrangements that can be formed using the letters in the word CHEESECAKE? Answer:

What is the total number of different 1010-letter arrangements that can be formed using the letters in the word CHEESECAKE?\newlineAnswer:

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Full solution

Q. What is the total number of different 1010-letter arrangements that can be formed using the letters in the word CHEESECAKE?\newlineAnswer:
  1. Count Letters: Count the number of each letter in CHEESECAKE: C=2C=2, H=1H=1, E=3E=3, S=1S=1, K=1K=1, A=1A=1, E=3E=3 (already counted).
  2. Calculate Total Factorial: Calculate the factorial of the total number of letters: 10!10! for the different arrangements if all letters were unique.
  3. Divide by Repeating Factorials: Divide by the factorial of the number of times each letter repeats to correct for overcounting: divide by 2!2! for CC and 3!3! for EE.
  4. Perform Calculation: Perform the calculation: 10!/(2!∗3!)=3,628,800/(2∗6)=3,628,800/12=302,40010! / (2! * 3!) = 3,628,800 / (2 * 6) = 3,628,800 / 12 = 302,400.

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