The total number of ways a paper/ink choice combination could come out is given by p*i. So, it's 42. You seem to know that already.
So, the chance of any one of those choices coming up is 1/42. You need to figure out the probability that two paper/ink choices will come out a certain way.
The choices made in one event to not affect the probability of any given choice coming up in a second event. So, the probability of the first event happening the way it did is 1/42, and the probability of the second happening the way it did is also 1/42.
I think that, to put them together, you multiply them. This comes out 1/1764, like you said. Your teacher appears to have simply multiplied by the number of events (2), giving 1/21. That would mean that, as you add more events, the likelihood of any given series of events coming out a certain way increases, which just makes no sense at all.
To see why, imagine flipping a coin. The probability that a certain face will come up is 1/2. If you want the same face to come up again, the chances are (1/2)(1/2) = 1/4. If you were to multiply by the number of events (2), you would get a probability of 1. This would mean that a coin, once flipped, *must* turn up the same face in all subsequent flips. This is clearly not the case, and if your teacher disagrees with you, ask him if he's ever flipped a coin before.
I mean, I could be wrong, of course. Anyone?