Question -
Answer -
Given:
The word ‘ORIENTAL’
Number of vowels inthe word ‘ORIENTAL’ = 4(O, I, E, A)
Number of consonantsin given word = 4(R, N, T, L)
Odd positions are (1,3, 5 or 7)
Four vowels can bearranged in these 4 odd places in 4P4 ways.
Remaining 4 evenplaces (2,4,6,8) are to be occupied by the 4 consonants in 4P4 ways.
So, by using theformula,
P (n, r) = n!/(n – r)!
P (4, 4) × P (4, 4) =4!/(4 – 4)! × 4!/(4 – 4)!
= 4! × 4!
= 4 × 3 × 2 × 1 × 4 ×3 × 2 × 1
= 24 × 24
= 576
Hence, the number ofarrangements so that the vowels occupy only odd positions is 576.