Answer: 118 combinations.
Explanation:
In ALIVE we have 5 letters, rearranging it we have the possible options of:
5 options for the first letter.
4 options for the second letter, as one was already chosen for the first one
3 options for the third letter, as 2 were already chosen.
2 options for the fourth letter.
1 option for the last letter.
The total number of combinations will be equal to the product of the numbers of options for each letter, then we have:
5*4*3*2*1 = 120 combinations.
And the combinations where the word EVIL is formed are:
AEVIL
EVILA
2 combinations, then the total number of combinations such that the word evil is not formed are:
120 - 2 = 118 combinations.