At Whatsamatta U, 30% of the math majors are classified as minorities. FInd the probability that, in a random sample of ten physics majors, no more than six are classed as such.

Would I use the formula "P(x)= C(n,x) * p^(x) * q^(n-x)"? Also, would P be 0.3?

You've got the right formula. Note that you'll need to find the probability for each of the cases of "exactly zero" through "exactly six", and sum them to find the probability of "no more than six", which also means "six or fewer".

Or else (which should be less work) find the probabilities of "exactly seven" through "exactly ten", sum them, and subtract from "1".

It's a bit of a slog, either way...