Question 40624
Lay out all possible 1st letters in the 3-letter word
O
L
I
V
E
What are the choices for the 2nd letter in each case?
O and any one of the remaining 4 letters L,I,V,or E
L and any one of the remaining 4 letters O,I,V,or E
I and any one of the remaining 4 letters O,L,V,or E
V and any one of the remaining 4 letters O,L,I,or E
E and any one of the remaining 4 letters O,L,I,or V
So, for each of 5 possible 1st letters, ther are 4 possible 
2nd letters. That makes 5 x 4 = 20 possibilities so far
Now include the possibilities for the 3rd letter
O AND any one of the remaining 4 letters L,I,V,or E AND one of 3 letters left
L AND any one of the remaining 4 letters O,I,V,or E AND one of 3 letters left
I AND any one of the remaining 4 letters O,L,V,or E AND one of 3 letters left
V AND any one of the remaining 4 letters O,L,I,or E AND one of 3 letters left
E AND any one of the remaining 4 letters O,L,I,or V AND one of 3 letters left
For each of the 4 2nd letters on each line, there are 3 possible
3rd letters 
O AND 4 X 3 possible 2nd and 3rd letters
L AND 4 x 3 possible 2nd and 3rd letters
I AND 4 X 3 possible 2nd and 3rd letters
V AND 4 x 3 possible 2nd and 3rd letters
E AND 4 x 3 possible 2nd and 3rd letters
The toal is 5 x 4 x 3 = 60 possible 3 letter words from olive