Question

The no. of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants?

Answer 1

Here is example for your question:-

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

A) In word ARTICLE.There are 3 vowels and 4 consonants

Total no of letters =7

Total no of even place =3

There are 3 vowels to be filled in 3 places

Hence the no of ways =3C3=13C3=1

The vowels can arrange among themselves in 3! ways

⇒6⇒6

Now the four consonants can fill the remaining 4 places in =4!

⇒4×3×2×1⇒4×3×2×1

⇒24⇒24

The total no of words formed =1×6×241×6×24

⇒144⇒144 ways

Answer 2

the answer is 144
which is 6*24