Incorrect. Our third term in the sum was a little bit off, otherwise we would have obtained the correct answer.
Incorrect. Our numerator included the 6 combinations with the two disliked flavors, times the three possible toppings. However, we did not add three for the remaining three flavors if topped with chocolate chips. Our denominator was correct.
We inadvertently converted half a foot (0.5 ft) to 5 inches instead of 6 inches, which would have given us the correct answer.
From the last day of school, we overcounted the number of days remaining in June by one. We also carried over our incorrect answer from part two. Otherwise, we would have calculated the correct answer.
Incorrect. I misinterpreted the problem as the number of different sequences of the last 5 fireworks out of the 15 available. Rather, those five were already determined. Therefore, instead of the number of permutations of 15 items arranged 5 at a time, the problem asks for the number of ways to arrange the remaining 10 fireworks.
Approximately correct. Overlooking the last sentence, which asks for the answer to be rounded to the nearest tenth, I instead rounded up to the nearest whole number.
Incorrect. My solution counted permutations rather than combinations. The number of combinations is small enough that they can quickly be listed and counted.
Incorrect. At the time, I could not figure out how to solve the problem. In hindsight, I could have solved it by using one of my favorite techniques: a table diagram. In the image below, I constructed a 10 x 10 table to see which of the first 10 lockers are closed after the first ten students exited the school. The result is that only the lockers numbered as perfect squares were closed. Assuming that this pattern continues to the 900th locker, it is a safe guess that all lockers numbered as perfect squares will be the only ones that are closed. It is also interesting to observe that the total number of lockers, 900, is a perfect square. The square root of 900 is 30, which means there are a total of 30 perfect squares from 1 to 30.