Given:

The word ‘ORIENTAL’

Number of vowels in the word ‘ORIENTAL’ = 4(O, I, E, A)

Number of consonants in given word = 4(R, N, T, L)

Odd positions are (1, 3, 5 or 7)

Four vowels can be arranged in these 4 odd places in ^{4}P_{4} ways.

Remaining 4 even places (2,4,6,8) are to be occupied by the 4 consonants in ^{4}P_{4} ways.

P (4, 4) × P (4, 4) = \(\dfrac{ 4!}{(4 – 4)!} × \dfrac{4!}{(4 – 4)!}\)

= 4! × 4!

= 4 × 3 × 2 × 1 × 4 × 3 × 2 × 1

= 24 × 24

= 576

Hence, the number of arrangements so that the vowels occupy only odd positions is 576.

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