How to get all possible combination With the total number of possible combination for "n" variables that can take different values

Hi Guys,

I have "n" variables that my take different values each. (e.g.: length of variable 1 = m1, 2 = m2, 3 = m3 , ...., n = mn)

how can i get the following:

1- what is the total number of possible combination for such problem? is that m1*m2*m3*.....*mn?

2- is there an easy way to get the totale possible combination as a table for those n variables? something like this:

Comb-1 Comb-2 .....................

Var(1) Val(Var(1)[1]) Val(Var(1)[2])

Var(2) Val(Var(2)[1]) Val(Var(2)[1])

Var(3) Val(Var(3)[1]) Val(Var(3)[1])

. . .

. . .

. . .

Var(n) Val(Var(n)[1]) Val(Var(n)[1])

Thanks in Advance

Answer 1

[Bruno Luong]

Checkout similar thread

https://www.mathworks.com/matlabcentral/answers/476022-how-to-pick-up-all-combination-of-numbers-from-multiple-vectors?s_tid=srchtitle

[Aubai]

somehow did not see that thanks for sharing and helping

Answer 2

[Voss]

a = [1 99];
b = [2 30 700];
c = [4 55 666 8888];

vars = {a,b,c};
n = numel(vars);
out = cell(1,n);
[out{:}] = ndgrid(vars{:});
result = reshape(cat(n+1,out{:}),[],n);

disp(result)

           1           2           4
          99           2           4
           1          30           4
          99          30           4
           1         700           4
          99         700           4
           1           2          55
          99           2          55
           1          30          55
          99          30          55
           1         700          55
          99         700          55
           1           2         666
          99           2         666
           1          30         666
          99          30         666
           1         700         666
          99         700         666
           1           2        8888
          99           2        8888
           1          30        8888
          99          30        8888
           1         700        8888
          99         700        8888

Transpose result if desired.

An option for R2023a or later is to use the combinations function:

result = combinations(a,b,c); % R2023a or later

disp(result)

    a      b      c  
    __    ___    ____

     1      2       4
     1      2      55
     1      2     666
     1      2    8888
     1     30       4
     1     30      55
     1     30     666
     1     30    8888
     1    700       4
     1    700      55
     1    700     666
     1    700    8888
    99      2       4
    99      2      55
    99      2     666
    99      2    8888
    99     30       4
    99     30      55
    99     30     666
    99     30    8888
    99    700       4
    99    700      55
    99    700     666
    99    700    8888