In a class of students, 80 spoke English, 110 spoke spanish, 100 spoke french, 50 spoke english & spanish, 30 spoke english & french, 20 spoke french & spanish, 10 spoke english & frnech, but no spanish.

How many spoke spanish & french, but not english?

The answer is 0. I was wondering how this is the case.

Mistyped it should say "10 spoke english & french" not "10 spoke english & frnech"

If 30 spoke E&F and 10 spoke E&F but not S, then that means 20 spoke E,F,S.

So, in your Venn diagram, the small triple intersection in the center has a 20 in it.

But, since only 20 spoke French and Spanish, and all of them also spoke English, there are 0 who spoke no English.

Thank you!

To find out how many students spoke Spanish and French but not English, we can use a method called the Inclusion-Exclusion principle.

According to the given information:
- 80 students spoke English.
- 110 students spoke Spanish.
- 100 students spoke French.
- 50 students spoke English and Spanish.
- 30 students spoke English and French.
- 20 students spoke French and Spanish.
- 10 students spoke English and French but not Spanish.

To find the number of students who spoke Spanish and French but not English, we need to subtract the number of students who spoke Spanish, French, and English from the total number of students who spoke Spanish and French.

Let's calculate step by step:

1. Start with the total number of students who spoke Spanish and French:
- 20 students spoke French and Spanish.

2. Subtract the number of students who spoke French, Spanish, and English:
- 10 students spoke English, French, and Spanish.

Therefore, the number of students who spoke Spanish and French but not English is 20 - 10 = 10.

So, the correct answer is 10, not 0.