Question

How many words can be formed from the letters of the words ARTICLE, if vowels always come at the odd places:

• A. $60$
• B. $576$
• C. $\frac{7!}{3!}$
• D. $120$

Answer 1

Answer: (B)

$576$

In word ARTICLE , there are 3 vowels and 4 consonents

Total no. of letters$=7$

Total no. of odd places$=4$

There are 3 vowels to be filled in 4 places

Hence the no. of ways$={}^4{C}_3=\frac{4!}{3!(4-3)!}=4$

The vowels can arrange among themselves in $4!$ ways$=4\times 3\times 2\times 1=24$

Now the four consonants can fill in the remaining 3 places in$=3!=3\times 2\times 1=6$

Total no. of words formed$=4\times 24\times 6=576$