How many arrangements of the letters in MEADOWS place vowels in even positions?
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Answer: B. 144
Explanation
The word meadow contains seven total letters, featuring three vowels and four distinct consonants. Arranging the three vowels into the three available even positions can be done in exactly six different ways. Placing the remaining four consonants into the four odd positions allows twenty-four permutations, yielding one hundred forty-four total arrangements. Permutations calculate the number of possible ways to order a subset of items where sequence matters significantly. Factorial notation denotes the product of an integer and all the positive integers descending below it. The fundamental counting principle states that if there are ways to do one thing and ways to do another, you multiply them.
Option A represents the total factorial of all seven letters without restricting vowels to even positions. Option C miscalculates the product of the vowel and consonant permutations by omitting crucial factorial steps. Option D underestimates the total combinations by failing to account for all valid consonant placement positions.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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