Question 159
Professor Carlão decided to write a math problem worth 10 points in total, with three parts: $a, b$ and $c$. After writing the parts, he was unsure about the best way to distribute the 10 points among the parts so that each is worth a positive integer number of points.
a) Joana, a teacher friend of Carlão, suggested that part $c$ should be worth the same number of points as the sum of parts $a$ and $b$ since, according to her, part $c$ is harder. If Carlão follows Joana's suggestion, in how many different ways can he distribute the points?
b) Disregarding Joana's suggestion, that is, assuming that Carlão will distribute the points in any way, in how many different ways can he distribute the 10 points of the problem among the three parts?
a) Joana, a teacher friend of Carlão, suggested that part $c$ should be worth the same number of points as the sum of parts $a$ and $b$ since, according to her, part $c$ is harder. If Carlão follows Joana's suggestion, in how many different ways can he distribute the points?
b) Disregarding Joana's suggestion, that is, assuming that Carlão will distribute the points in any way, in how many different ways can he distribute the 10 points of the problem among the three parts?