The probability that patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive?

This is a binomial probability problem. Given the probability that something occurs is p, then the probability that the thing does not occur is (1- p). And the probability that p occurs exactly k times out of n trials is:


P(k) = C(n,k)(p)^k(1-p)^{n-k}


For your problem p = 0.9, k = 5 and n = 7. Can you take it from here?