The number of four letter words can be formed from the letters of the word INFINITY so that 3 are alike, one is different is 

In the word INFINITY

There are III, NN, F,T,Y.

4 letter words to be formed using 3 like, one different letter

Fourth letter can be selected from { N,F,T,Y } in $4{\mathrm{C}}_1$ ways.

$\mathrm{No}.\mathrm{of} 4 \mathrm{letter} \mathrm{words}=4{\mathrm{C}}_1\times \frac{4!}{3!}=4\times 4=16.$