This is similar to Section 6.1 Problem 32: For_f(x,y)=6x7−4y7+7x³−7xªy³ :

Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once.  (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.

In a famous study done in the 1960s two dolphins, Doris and Buzz, were trained to work together to earn fish. Doris was shown a light underwater. If the light was on steadily, her partner Buzz on the other side of the tank needed to press a button on the right for them to earn fish. If the light was blinking, he needed to press a button on the left. At one point in the study, the researcher hung a canvas in the middle of the tank in such a way that Buzz could not see the light. After looking at the light, Doris "swam near the curtain and began to whistle loudly. Shortly after that Buzz whistled back and then pressed the correct button". (Tintle, Rossman and Chance, MAA Prep Workshop) Of course, getting it right once was not enough to convince the scientists that there was really communication going on. It turned out, that in 15 out of 16 trials the dolphin pushed the correct button. Of course, it is possible that this happened just out of random chance - that the second dolphin just…

List 5 outcomes that are in this sample space.

What is a Premutation Rule (when some items are different)?

Unfortunately, for some reason, at least one of the answers isn't correct. I got the same answeres myself. Is there a reason any could be wrong?

What is the “method of false position”, and how does it work?