Concept: The question tests on the basics of Counting
PENCILS has 7 letters
If 3 letters are to come between E and I, we can have the following for E and I
E _ _ _ I _ _ or _E _ _ _ I _ or _ _E _ _ _ I. There are 3 ways with E first then I and another 3 ways for I first and then E. Total 6 ways.
the remaining 5 letters can be arranged in 5! = 120 ways.
Total number of words = 6 * 120 = 720