Thread: Possibilities in a given set

There are 3 men A,B and C. They have 4 sons in total.
What are the total possibilities of the order of no. of sons they have.
How do we find it.
Plz help I am totally new to this topic.

Originally Posted by AaPa

There are 3 men A,B and C. They have 4 sons in total.
What are the total possibilities of the order of no. of sons they have.
How do we find it.

Solve in the non-negative integers.
We can put N identical objects into K different cells in
ways.
Here which is which?

Originally Posted by Plato

ways.

I don't understand this. I am not being taught this anywhere.
It just came to my mind randomly.

Originally Posted by AaPa

I don't understand this. I am not being taught this anywhere.
It just came to my mind randomly.

Well then make a list:
400
310
301
220
etc

But I wanted to do it using a formula.

Plato gave you "the formula"...
go read up:
Introduction to Combinations | | Mathematics and MultimediaMathematics and Multimedia

thanks a lot.

N=4 sons (1234) to separate into K=3 groups, using K-1=2 dividers (--).
So 123-4- means 3,1,0
So 1-23-4 means 1,2,1
So we have to choose K-1=2 dividers among N+K-1=4+2=6 symbols,
so #ways is (6 over 2), or (4+3-1 over 2), or (N+K-1 over K-1), or (N+K-1 over N)

Ya; and to "see them" as Plato suggested, just write 'em down in ascending order:
004
013
022
031
040....5
103
112
121
130....4
202
211
220....3
301
310....2
400....1
.........15