NEED HELP WITH MATH HOMEWORK!!!! PLEASE HELP ME! *10 POINTS FOR BEST ANSWER*!!!

Hi, I don't understand my math hw. I need to know this for a test, so can you please show me how to do this? By that I mean show work and how you did it. thank you :DD<333

. In a group of 30 high school students, 8 take French, 12 take Spanish, and 3 take both languages. How many students of the group take neither French nor Spanish?

Drawing a "Venn Diagram" is helpful here, though I can't really draw in text here, so just draw two circles that intersect. The first circle represents the French speaking students, the second circle represents the spanish taking students. Put a "3" in the space where the two circles intersect. This is where the "both" section is. There are 8 students total in the first circle, including in the interescting area. So there are 5 students in the circle outside the intersecting area. Put a "5" in that area. In the second circle there should be 12 students total, but 3 are in the intersecting area, so there are 9 others. Put a "9" in the part of the second circle outside the intersecting area. So so far you have 5 + 3 + 9 total students that take at least one language, 5 + 3 + 9 = 17. There are therefore 13 students outside the circles, put a "13" in the picture outside the circles.

Draw a big rectangle. Inside draw 2 small circles so that a small part of the one is inside the other. In other words to have a common area. This is know as Venn Diagram

This is your case. The intersection of the two circles (name the 1st F and the 2nd C) is the number of students that take both French and Spanish. You are looking for the area (number of students that are outside the circles and inside the rectangle.

As you should now from formula in probability for combined events is:

n(F or S) = n(F) + P(S) - n(F and S)

n(F or S) = 8 + 12 - 3

n(F or S) = 17 (note that n means number)