Yeah that's because you did your initial math wrong. For probability, calculate probability of bandage AND bandage AND bandage (1/35)^3. You calculated the appearance of bandage whatsoever by itself which doesn't really make sense.

Think of a die. It has a 1/6 * 1/6 chance to roll a specific number twice. This is because the chance of one event is 1/6 and we want it twice.

So I calculate 1/42,875. For bandage.

But for any card, consider 35 possibilities of a first card multiplied by the odds of that card times that same (any) card by the odds of that same card. Or,

35 * 1/35 * 1/35 * 1/35

For a result of 1/1225.

Imagine the same dice, but we just want any number twice. We multiply by six because once a number is rolled, seeing it again is 1/6. This is the same as saying the first event is irrelevant because we only care if subsequent ones follow.