$|A \cup B| = |A|+|B| - |A \cap B|$
$|\text{combinatorics or algebra}]| = |\text{combinatorics}|+|\text{algebra}| - |\text{combinatorics and algebra}| = 75 + 60 - 25 = 110$
$P[\text{combinatorics or algebra}] = \dfrac{110}{150} = \dfrac{11}{15}$
$\text{neither combinatorics nor algebra} = \neg \text{combinatorics} \cap \neg \text{algebra}$
$|\neg \text{combinatorics} \cup \neg \text{algebra}| = 150 - |\text{combinatorics or algebra}| = 150 - 110 = 40$
$P[\text{neither combinatorics nor algebra}] = \dfrac{40}{150} = \dfrac{4}{15}$
Looks like you did it correctly. Well done!