Apassword must consist of 16 characters. each character can be a digit(0-9), an uppercase or lowercase letter (a-z, a-z) or one out of 10 specialcharacters. how many valid passwords are there? if you have forgotten your password, but can test 1 trillion passwords persecond, how much time would you require to find the password in theworst-case scenario that your forgotten password is the last one tested? give the answer in years, rounded to the nearest power of 10.

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.)