Case Eastern Junior College awarded 26 varsity letters in crew, 15 in swimming, and 16 in scoccer. If awards went to 46 students and only 2 lettered in all sports, how many students lettered in two of the three sports?

after subtracting 2 from each category,

24 in crew, 13 in swimming, 14 in soccor

or 51 total. You have already given away six letters, so you have 44 students, seven less than the total letters to give away. So seven of those must go to duplicate awardees.

check my thinking.

To find the number of students who lettered in two of the three sports, we can use the principle of inclusion-exclusion.

Step 1: Find the total number of students who lettered in at least one sport.
To do this, add the number of students who lettered in each individual sport: 26 (crew) + 15 (swimming) + 16 (soccer) = 57.

Step 2: Find the number of students who lettered in all three sports.
Given that only 2 students lettered in all sports, subtract that from the total in step 1: 57 - 2 = 55.

Step 3: Find the number of students who lettered in exactly two of the three sports.
We can use the principle of inclusion-exclusion to find this by subtracting the number of students who lettered in all three sports from the total number of students who lettered in at least one sport: 55 - 2 = 53.

Therefore, there are 53 students who lettered in two of the three sports.