Question

The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is

Answer 1

In word ARTICLE, there are 3 vowels and 4 consonants.

Total number of letters = 7

Total number of even place =3

There are 3 vowels to be filled in 3 places.

Hence, the number of ways = ${3_C}_3=1$

The vowels can arrange among themselves in $3!=6$ ways.

Now, the 4 consonants can fill the remaining 4 places in $4!=24$ ways.

Therefore, total number of ways = $1\times 6\times 24=144ways$.