There are 30 flavors and you can mix up to 3 of them. how many flavor possibilities are there? you can't mix the same flavors more than once in one drink. show your work.

What is the greatest number of parts of a circle that can be formed by cutting the circle with 7 straight cuts? (note: the parts do not have to be equal in size)

If value of cos330° is √3/2 then find tan165°.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?