A spot light illuminates a circular spot on a stage and can be represented by the equation (x – 13)² + (y – 4)2 = 16. Joel is standing at (11,4) and
Amerra is at (8,5). Are they both in the spotlight?
Joel is the only one in the spotlight
Amerra is the only one in the spotlight
Both are in the spotlight
Neither are in the spotlight
Activate

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)