# Math Help - Inclusion-Exclusion theorm

1. ## Inclusion-Exclusion theorm

Any help would be appreciated...I'm rather stuck!
It's a mock exam and annoyingly they provided no solutions for me to work from...grrr....

Thank-you

2. Inclusion

Solution for 1a in line 2.

For 1b think a little!

3. Originally Posted by Also sprach Zarathustra
Inclusion

Solution for 1a in line 2.

For 1b think a little!
I'll type out what i've written =)...the main problem i'm having is i don't know if it is right! Or even how i'm doing it is right...
ty for reply

4. Using the floor function there $\left\lfloor {\frac{{50}}
{3}} \right\rfloor = 16$
of those 50 numbers divisible by 3.

5. Originally Posted by Plato
Using the floor function there $\left\lfloor {\frac{{50}}
{3}} \right\rfloor = 16$
of those 50 numbers divisible by 3.
But then how would it be possible to work out without writing out all the numbers(for example A n B)? I was under the impression the question should be calculated without doing that?

Thanks

6. Originally Posted by AshleyT
But then how would it be possible to work out without writing out all the numbers(for example A n B)? I was under the impression the question should be calculated without doing that?
It is not possible to do that easily.

7. Originally Posted by Plato
It is not possible to do that easily.
So i would have to go through and write all the numbers out basically?
I don't see the point of that using the inclusion-exclusion theorm...arg...this is the annoying thing about not having the solutions...don't know how they want us to do it...

Thankyou for your reply Plato

EDIT: WAIT NEVER MIND I GET IT NOW!! Silly me was thinking it was the actual numbers, rather than how many were in the set!

Thankyou!!

8. Originally Posted by AshleyT
So i would have to go through and write all the numbers out basically?
I don't see the point of that using the inclusion-exclusion theorm...arg...this is the annoying thing about not having the solutions...don't know how they want us to do it.
The answer is clear:
$\left\lfloor {\frac{{50}}
{2}} \right\rfloor + \left\lfloor {\frac{{50}}
{3}} \right\rfloor + \left\lfloor {\frac{{50}}
{5}} \right\rfloor - \left\lfloor {\frac{{50}}
{6}} \right\rfloor - \left\lfloor {\frac{{50}}
{{10}}} \right\rfloor - \left\lfloor {\frac{{50}}
{{15}}} \right\rfloor + \left\lfloor {\frac{{50}}
{{30}}} \right\rfloor$

That is using the inclusion-exclusion.

9. Hey, sorry i just edited my post before i saw your reply! I was misreading the formula... and i was working with a friend who said we should be writing out the numbers lol...

Thankyou for your help plato =)