Question

How many seven letter words can be formed without repetition out of the letters of the word ${}^{\prime }MISTAK{E}^{\prime }$ such that the vowels go only into the odd places

• A. $480$
• B. $786$
• C. $625$
• D. $576$

Answer 1

The correct option is D $576$

There are four odd places and three vowels. We can arrange the vowels in ${}^4{P}_3$ ways. The other four placces can be then filled in by the remaining four letters in $4!$ ways. Thus ${}^4{P}_3\times 4!=576$ words