Select all the statements about functions g(x)=x2−4x+3andf(x)=x2−4x that are true. 1.The vertex of the graph of function g is above the vertex of the graph of function f.

2.The graphs have the same axis of symmetry.

3.Function f has a maximum value and function g has a minimum value.

4.The graphs never intersect.

5.The graphs have the same y-intercept.

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.)