Define the double factorial of n, denoted , as follows: ={1⋅3⋅5(n−2)⋅nif n is odd 2⋅4⋅6(n−2)⋅nif n is even and (−1)==1. find the radius of convergence for the given power series. ∑n=1[infinity]3n⋅n! ⋅(5n+8)! ⋅(2n)⋅[(n+9)! ]5⋅(4n−4)(−6x+4)n the radius of convergence, r

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.)