# Finding total number of combinations which include some specific numbers

• Apr 26th 2013, 03:19 PM
Awareness
Finding total number of combinations which include some specific numbers
My math is not good and I am not sure in which forum section I should post my question.

Let's say I want to group numbers between 1 and 50 with 4 columns:
1 2 3 4
1 2 3 5
1 2 3 6
...
2 3 4 5
2 3 4 6
...
47 48 49 50

To find the total possible combinations,we do:
50*49*48*47
__________
1*2*3*4
This formula gives the maximum possible combinations.

My question is,what would the formula be to find maximum of how many combinations of
these numbers include number 1 and 2(for example)?
• Apr 26th 2013, 07:53 PM
chiro
Re: Finding total number of combinations which include some specific numbers
Hey Awareness.

You would need to just restrict the state space to those which have a 1 and 2.

Hint: Take a look at this formula:

Inclusion?exclusion principle - Wikipedia, the free encyclopedia
• Apr 26th 2013, 08:15 PM
Plato
Re: Finding total number of combinations which include some specific numbers
Quote:

Originally Posted by Awareness
My math is not good and I am not sure in which forum section I should post my question.
Let's say I want to group numbers between 1 and 50 with 4 columns:
1 2 3 4
1 2 3 5
1 2 3 6...
2 3 4 5
2 3 4 6
...
47 48 49 50

To find the total possible combinations,we do:
50*49*48*47
__________
1*2*3*4
This formula gives the maximum possible combinations.
My question is,what would the formula be to find maximum of how many combinations of
these numbers include number 1 and 2(for example)?

There are so many difficulties with this qauestion that there no good place to start.
FIRST: neither 1 nor 50 is between 1 and 50.
If you want include them then say numbers from 1 to 50.

With that linguistic understanding then your numbers look like $\boxed{~A~}\boxed{~B~}\boxed{~C~}\boxed{~D~}$

There are 50 choices for A, 49 choices for B, 48 choices for C, and 47 choices for D.