Q. How many words can be formed from the letters of the word ARTICLE, if vowels always comes at the odd places?
A) 60
B) 576
C) $\frac{7!}{3!}$
D) 120
Explanation
(b)
In a word ARTICLE, there are 7 letters. Out of 7 places, 4 places are odd and 3 even. Therefore 3 vowels can be arranged in 4 odd places in $\ ^{4}P_{3}$ ways and remaining 4 consonants can be arranged in $\ ^{4}P_{4}$ways. Hence, required number of ways $= \ ^{4}P_{3} \times {\ ^{4}P}_{4} = 576$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.