How many words can be formed out of the letters of the word, ARTICLE, so that vowels occupy even places?

Options

A. 1440
B. 144
C. `7"!"`
D. `""^(4)C_(4) xx ""^(3)C_(3)`

Answer

B

Explanation

Total number of letters in the word article is 7, out of which A, E, I are vowels and R, T, C, L are consonants.
Since, it is given that vowels occupy even place, therefore the arrangement of vowel, consonant can be understand with the help of following diagram.
`{:(1, 2, 3, 4, 5, 6, 7):}`
Now, vowels can be placed at 2, 4 and 6th position.
Therefore, number of arrangement `= ""^(3)P_(3) = 3"!" = 6` ways
and consonants can be placed at 1, 3, 5 and 7th position.
Therefore, number of arrangement `= ""^(4)P_(4) = 4"!" = 24`
`therefore` Total number of words `= 6 xx 24 = 144`