Question:
The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
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Use complementary counting and multinomial coefficients for words with repeated letters.
Updated On: Oct 16, 2025
- 2025
- 2765
- 3265
- 3205
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The Correct Option is D
Solution and Explanation
Step 1: Total letters in INCONVENIENCE
Letters and their counts: \[ I(3), N(3), C(2), O(1), V(1), E(2) \] Step 2: Total possible 5-letter words
Calculate total 5-letter arrangements considering repetitions. Step 3: Calculate number of 5-letter words with no repeated letters
Calculate using only distinct letters. Step 4: Use complementary counting
Number with at least one repeated letter = Total 5-letter words - Number with all distinct letters. Result is 3205.
Letters and their counts: \[ I(3), N(3), C(2), O(1), V(1), E(2) \] Step 2: Total possible 5-letter words
Calculate total 5-letter arrangements considering repetitions. Step 3: Calculate number of 5-letter words with no repeated letters
Calculate using only distinct letters. Step 4: Use complementary counting
Number with at least one repeated letter = Total 5-letter words - Number with all distinct letters. Result is 3205.
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