Just started S1, just wondering if you could help me out with this question?

Many thanks

Then500 people own a fish, dog or cat. Of this, 314 own a fish, 228 own a dog and 312 own a cat. of these, 160 own a fish and a dog, 100 own a dog and a cat, 134 own a cat and a fish. calculate the number which own all 3 pets

tried:By using set notation, express these 3 events as at least two of these events occurring.

500 = F + (C-(C n F)) + (D - (D n F)) - (D n C) + (ALL3)

This gives me a silly answer so must be wrong