How many new arrangements can be created using the letters of the word 'ALIVE'__________?
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Answer: C. 119
Explanation
The word alive consists of five completely distinct letters, allowing five factorial total arrangements. Calculating five factorial produces a total of one hundred twenty possible letter permutations. Subtracting the single original arrangement from the total yields one hundred nineteen brand new arrangements. Word anagram problems test the application of factorial mathematics to reorder sequences of distinct alphabetical characters. Distinct items can be arranged in linear sequences using standard factorial formulas without repetition complications. Finding new arrangements always requires removing the initial baseline sequence from the total calculated permutation count.
Word games and puzzle designers use anagram calculations to determine difficulty levels for language challenges. Data compression algorithms analyze character permutations to optimize storage efficiency for textual information files. Linguists study letter frequency and arrangement possibilities to understand structural patterns within human languages. Option A represents four factorial instead of five, ignoring the complete length of the word. Option B forgets to subtract the original word arrangement from the total calculated permutation count. Option D forgets to subtract the original sequence, mistakenly providing the total permutation count instead.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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