Which statements are true? 1. 20 is the greatest common factor of 40 and 80.

2. 64 is a perfect square.

3. x(x^2+1)=x^3+x

4. x^2-81 cannot be factored

5. 3x^3 is the GCF of 15x^4+9x^2+3

6. (x+5) is a factor of x^2-2x+15

7. (4x^2+2)(x^2-2)=4x^4-6x^2-4

8. x+3 is a factor of x^2+9

9. The product of two binomials is always a trinomial.

10. 57 is a prime number.

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.)