A company that sells phones has received complaints from customers that their certain new types of phones cracks at a temperature of over 38⁰C. they decide to test sample of 100 phones by putting them at this temperature. the sample tests revealed that 30% of the phones cracked. because the company did not test all this type of phones due to potential destructive testing, they are interested in using the sample test to estimate the results had all phones been tested a how many phones should have been tested for the percentage of phones that cracked to be within +-4% with a 95% confidence interval?​

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.)