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)?

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

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 $\displaystyle \boxed{~A~}\boxed{~B~}\boxed{~C~}\boxed{~D~}$

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