List of all Binomial permutations with a certain number of events

Hello there,

I am trying to do something very simple I think and have come across this problem I cannot solve. I am not proficient with matlab.

All I want to do is to find all the possible permutation of tossing a coin 8 times where we ONLY have 4 heads and 4 tails. All of the possible combinations for only this scenario, the order does not matter.

so something like

1) H H H H T T T T

2) H H T T H H T T

3) H T T H H T H T

and so on....

Answer 1

[Torsten]

n = 8;
A = dec2bin(0:2^n-1)-'0'

A = 256×8

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1

A4 = A(sum(A,2) == 4,:)

A4 = 70×8

0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1

8*7*6*5/(4*3*2*1)

ans = 70

% more general
Ai = arrayfun(@(i)A(sum(A,2) == i,:),0:n,'UniformOutput',0)

Ai = 1×9 cell array
    {[0 0 0 0 0 0 0 0]}    {8×8 double}    {28×8 double}    {56×8 double}    {70×8 double}    {56×8 double}    {28×8 double}    {8×8 double}    {[1 1 1 1 1 1 1 1]}

sum(arrayfun(@(i)size(Ai{i},1),1:n+1))

ans = 256

[Massimiliano Induberino]

Hello there,

thank you very much for the answer!

I think what I was looking for is A4 since this only has the combinations where 4 Hs and 4 Ts are present.

A4 has all the combination where this can happen.

Is that correct?

[Torsten]

Yes.

The code after the comment

% more general

lists the combinations with 0,1,2,3,4,...,8 heads in a row separately.

The total number of combinations is 2^8, and this comes out to be true after the splitting of the possible outcomes.