Utilizing every character in the string “THURSDAY”, how many distinct letter combinations can be generated?
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Answer: B. 8!
Explanation
The word THURSDAY contains eight unique letters with no character repetitions present anywhere. Arranging a set of distinct items requires calculating the factorial of the total count. The factorial of eight, denoted as eight exclamation mark, represents the correct permutation total. Permutations refer to the different possible ways of ordering a set of unique objects. The factorial function multiplies an integer by every positive integer below it sequentially. Because all letters are distinct, no division is required to remove duplicate arrangements.
Combinatorics and permutations are fundamental concepts in cryptography and secure password generation. Scheduling algorithms use permutations to evaluate every possible sequence of assembly tasks. Genetics applies permutation principles to analyze potential DNA nucleotide sequence arrangements. Option A confuses the total number of unique letters with the total number of permutations. Option C incorrectly subtracts one from the letter count before applying the factorial. Option D merely states the number of letters minus one without any factorial calculation.
- Subject
- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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