# Set Theory Problem

1. Aug 15, 2011

### Ascleipus

1. The problem statement, all variables and given/known data
There are 30 people in a class of which 7 people have black hair and 24 people are right handed. 2 people are neither right handed nor have black hair.
1. How many have black hair and are right handed?
2. How many have black hair and are not right handed?

I'm sure this is quite a simple question for many of you but I haven't covered all of set theory yet but I would really to know how to do it, it has to be solved using set theory.
2. Relevant equations
there are none

3. The attempt at a solution
Sorry I only know the basics please let me know how to solve it.

Thanks a lot

2. Aug 15, 2011

### ArcanaNoir

So we have 30 people.
24 are right handed, so that means 6 are left handed.
7 have black hair so that means 23 do not have black hair.

You want to account for the people you know both conditions about.

We know 2 are left handed and do not have black hair.
Since there are only 6 left handed people altogether, there must be 4 left handed people who have black hair.

The rest of the people are right handed.

How many people are right-handed?
How many of those people have black hair?

3. Aug 15, 2011

### Ascleipus

thanks a lot helped me greatly and actually helped me with problem solving in general, i always look on the one side rather than finding the other side (i.e. he number of left handed people). So thanks a lot i believe the answer to question 1 is 3 :)

4. Aug 15, 2011

### ArcanaNoir

You got it :)