Suppose Alice has 25 balls that she throws them one by one into k different buckets. Each ball has an equal probability of 1/k of landing in any of the buckets. Compute the probability that at least two balls end up in the same bucket for the following values of k.

The sat and act tests use very different grading scales. the sat math scores follow a normal distribution with mean 518 and standard deviation of 118. the act math scores follow a normal distribution with mean 20.7 and standard deviation of 5. suppose regan scores a 754 on the math portion of the sat. how much would her sister veronica need to score on the math portion of the act to meet or beat regan's score?