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How many different ways can the letters of the word offices be arranged so that all the vowels always come together?
Wiki User
∙ 12y ago
The different ways the vowels can be arranged together is 3x2x1 = 6.
The number of places this arrangement can go within the word is 5.
This means there are 30 possible arrangements for the vowels. The consonants can be arranged amongst themselves with 4 possibilities for first place, 3 for second, 2 for third and 1 for fourth. This gives us 4x3x2=24 combinations.
So with 30 possible arrangements for the vowels, and 24 for the consonants, this gives us 720 possible ways of arranging the letters in the word offices so that the vowels always come together.
Wiki User
∙ 12y ago
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