Answer :

**Given****:** the word is ‘ORIENTAL.’

**To find:** number of arrangements so that the vowels occupy only odd positions

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

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

Let vowels be denoted by V

Odd positions are 1, 3, 5 or 7

So, fix the position by vowels like this:

Now, arrange these 4 vowels at 4 places

**Formula used:**

Number of arrangements of n things taken all at a time = P(n, n)

∴ Total number of arrangements of vowels

= the number of arrangements of 4 things taken all at a time

= P(4, 4)

{∵ 0! = 1}

= 4!

= 4 × 3 × 2 × 1

= 24

The remaining 4 even places can be occupied by 4 consonants

So, arrange 4 consonants at remaining places

**Formula used:**

Number of arrangements of n things taken all at a time = P(n, n)

∴ Total number of arrangements of consonants

= the number of arrangements of 4 things taken all at a time

= P(4, 4)

{∵ 0! = 1}

= 4!

= 4 × 3 × 2 × 1

= 24

**Hence, the number of arrangements so that the vowels occupy only odd positions = 24 × 24 = 576**

Rate this question :

Four letters E, KRD Sharma - Mathematics

. There are 6 iteRD Sharma - Mathematics

How many permutatRD Sharma - Mathematics

Find the total nuRD Sharma - Mathematics

In how many ways RD Sharma - Mathematics

From among the 36RD Sharma - Mathematics

How many differenRD Sharma - Mathematics

How many three-diRD Sharma - Mathematics

In how many ways RD Sharma - Mathematics

How many three-diRD Sharma - Mathematics