For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, if your answer is the number of 6-permutations of a set with 10 elements, you should write P(10,6) or 10!/4! or 10 × 9 × 8 × 7 × 6 × 5, but not 151200. 3. A French pastry shop sells 15 different flavors of macarons. Assume that it has an unlimited supply of each type. How many ways are there to choose 12 macarons from these 15 flavors if... 3.1 ...they are all the same flavor? 3.2...they are all different flavors? 3.3 ...half are one flavor and half are a different flavor (for example, half are raspberry and half are chocolate)? 3.4...at most 4 are salted caramel? 3.5 ...at least 2 are pistachio and at least 4 are hazelnut?

The Sweet Encounter is a touring international candy festival. The festival's most popular product is rainbow lollipops. At one stop of the tour, the festival promoter took a sample of the products offered. He found that 14 of the 60 products in his sample were rainbow lollipops. Among the 960 products offered at that stop, 290 were rainbow lollipops. For the festival promoter's sample, find and write with proper notation the population proportion and sample proportion of products offered that were rainbow lollipops. Write the proportions as decimals (not percentages) rounded to two decimal places. (a) Population proportion: (Choose one) ? (b) Sample proportion: (Choose one) v

Simplify the expression O 5 O 5x O 5x² + 2x O 5x² - 2x O 25x² + 10x 25x²+10x 5x+2

Choose the correct elements in the set for the following: {y | y is an integer and y > -5}