Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1).

an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 are labeled negative x and 2 are labeled negative. 3 tiles are in the factor 2 spot: 2 are labeled + x and 1 is labeled negative. 12 tiles are in the product spot: 4 are labeled negative x squared, 4 are labeled negative x, 2 are labeled + x, and 2 are labeled +.
which is true regarding adi’s use of algebra tiles?

she used the algebra tiles correctly.
she did not represent the two original factors correctly on the headers.
the signs on some of the products are incorrect.
some of the products do not show the correct powers of x.

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.)