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How Many Words Can Be Formed Out of the Letters of the Word, 'Oriental', So that the Vowels Always Occupy the Odd Places? - Mathematics

How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?

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There are 8 letters in the word ORIENTAL.
We wish to find the total number of arrangements of these 8 letters so that the vowels occupy only odd positions.
There are 4 vowels and 4 odd positions.
These 4 vowels can be arranged in the 4 positions in 4! ways.
Now, the remaining 4 consonants can be arranged in the remaining 4 positions in 4! ways.
By fundamental principle of counting:
Total number of arrangements = 4!\[\times\]4! = 576

Concept: Factorial N (N!) Permutations and Combinations
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RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.4 | Q 4 | Page 37
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