SOLUTION: The freshman class at a college has a total of 250 students. One hundred and ten freshmen take math and 200 take English, while 75 take neither. How many freshman take both math an

Algebra.Com
Question 1127574: The freshman class at a college has a total of 250 students. One hundred and ten freshmen take math and 200 take English, while 75 take neither. How many freshman take both math and English?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
You have an universal set of 250 elements and two its subsets, M (=Math) of 110 elements and E (=English) of 200 elements.


The union of the subsets M and E contains 250-75 = 175 elements.


Now use the formula


    n(M U E) = n(M) + n(E) - n(M n E)


for the numbers of elements.


From this formula,


    n(M n E) = n(M) + n(E) - n(M U E) = 110 + 200 - 175 = 135.


Answer.  135 freshman take both Math and English.

--------------

To see many other similar solved problems,  look into the lesson
    - Counting elements in sub-sets of a given finite set
in this site.


RELATED QUESTIONS

Many colleges require students to take a placement exam to determine which math courses... (answered by greenestamps)
Probability-and-statistics: Last fall, a sample of n = 25 freshmen was selected to... (answered by stanbon)
A student is selected at random from a group of 200 students in which 135 take math, 85... (answered by stanbon)
Intersection and conditional probability Suppose that a certain college class contains... (answered by stanbon)
12. Last fall a sample of n=36 freshmen was selected to participate in a new four hour... (answered by stanbon)
This quarter, a survey of 110 students at De Anza College finds that 60 take math, 50... (answered by Edwin McCravy)
A survey of 100 students at New England College showed the following: 45 take English. (answered by ikleyn)
A freshman english class at a certain college has 49 women and 20 men. If 5 students are... (answered by stanbon)
Please show me how to solve this problem ( it was a homework problem (1 complete problem) (answered by solver91311)