The sandwich shop offers combo meals with a choice of one sandwich, one side, and one drink. on total there are 560 combos available. if there are 16 sandwiches and 5 drinks available, how many sides are there?

There are 7 sides available.

The fundamental counting principal tells us to find the total number of combinations of independent items, multiply the number of choices from each one (choices x choices x)

This means that drink x sides x sandwiches = 560.  We know there are 16 sandwiches and 5 drinks.  Let S be the number of sides:
15(6)(S) = 560
80S = 560

Divide both sides by 80:
80S = 560/80
S = 7

One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90$\%$ detection rate for carriers and a 5$\%$ detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual. (a) What is the probability that both tests yield the same result? (b) If both tests are positive, what is the probability that the selected individual is a carrier?