Question

How many words can be formed using all the letters of the word INTEGRAL so that the vowels occupy even positions?

• A. $720$
• B. $1,080$
• C. $2,880$
• D. $1,800$

Answer 1

Answer: (C)

$2,880$

We are given a word “INTEGRAL” out of which $3$ are vowels and $5$ are consonants.

Now we have to form all possible words from all its letters

such that vowels occupies even place i.e. vowels can only be placed at the position $2$,$4$,$6$ and $8$.

So we have $4$ places and $3$ vowels, so this could be done in

${}_4{C}_3\times 3!$

And remaining 5 places (including one even place) will be filled by 5 consonants in $5!$ ways.

So the total possible number of words are ${}_4{C}_3\times 3!\times 5!=4\times 3!\times 5!=4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1=2880$

Correct option is C