When Lino submitted an essay for his English class, it was 9 pages long. Lino's essay had errors on pages 2 and 7. If the teacher chose 3 pages uniformly at random to read, then the probability that she didn't read any of the pages with errors can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?
17
To solve this problem, we need to determine the probability that the teacher doesn't read any of the pages with errors. Let's break down the problem step by step:
Step 1: Calculate the total number of ways the teacher can choose 3 pages out of the 9-page essay. This can be done using combinations. In this case, we have 9 pages to choose from, and we need to choose 3, so the total number of combinations is given by:
C(9, 3) = 9! / (3! * (9-3)!) = 84
Step 2: Calculate the number of ways the teacher can choose 3 pages without any error pages. Since there are 2 error pages (pages 2 and 7), we can choose the remaining 3 pages from the 7 remaining pages. The number of combinations is given by:
C(7, 3) = 7! / (3! * (7-3)!) = 35
Step 3: Calculate the probability by dividing the number of ways to choose 3 pages without errors by the total number of combinations:
P = (Number of ways to choose 3 pages without errors) / (Total number of combinations)
= 35 / 84
Step 4: Simplify the fraction:
P = 35 / 84
= 5 / 12
So the probability that the teacher doesn't read any of the pages with errors is 5/12.
Finally, we need to find the sum of a and b, where a = 5 and b = 12:
a + b = 5 + 12 = 17
Therefore, the value of a + b is 17.