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What is the total number of different -letter arrangements that can be formed using the letters in the word PARADIGM?Answer:
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Q. What is the total number of different -letter arrangements that can be formed using the letters in the word PARADIGM?Answer:
- Identify Letters Count: Identify the number of each letter in the word PARADIGM.The word PARADIGM has letters with the following counts:P - , A - , R - , D - , I - , G - , M - .
- Calculate Total Arrangements: Calculate the total number of arrangements without considering the repetition of the letter 'A'.If all letters were distinct, the number of different arrangements of letters would be ( factorial)..
- Adjust for Repetition: Adjust for the repetition of the letter 'A'.Since the letter 'A' repeats twice, we need to divide the total number of arrangements by the number of ways to arrange these two 'A's among themselves to avoid overcounting.The number of ways to arrange two 'A's is ( factorial)..
- Calculate Final Arrangements: Calculate the final number of different arrangements.To find the total number of different -letter arrangements, divide the total number of arrangements from Step by the number of arrangements of repeated letters from Step .Total number of different arrangements = .
