The word INEFFECTIVE has following letters

 

                    E,E,E ; F,F ; I,I ; N,C,T,V

 

So the number of 4 letter words will be the coefficient of x⁴ in the expression

 

              4! ( 1 +  x/1 + x²/2 + x³/6)(1 +  x/1 + x²/2)²(1 + x)⁴

where the first term corresponds to how many times E would be taken. The x terms are divided by the factorial of the number of times they are taken because the alike letters will result in less permutations.

The second term corresponds to the number of times the F and I are taken and the last term corresponds to the number of times N,C,T,V are taken.

 

So find the coefficient of x⁴ to obtain the correct answer.

 

This is a general method and can be applied to any word.

 

Cheers