if I have the equation $$f(x_1,x_2,x_3,x_4)=x_1x_3+x_2x_4+x_1x_2x_4+x_1x_2x_3x_4$$
- How many equations are possible if two variables ?
when $x_1=x$ and the other four are y
when $x_2=x$ and the other four are y
when $x_3=x$ and the other four are y
when $x_4=x$ and the other four are y
I want to calculate the number of equations in each case
An example is if we have two variables. How many equation number we produce during compensation.
I suggest using combinations $C^2_4$ ... Is this true?
Can a program of work to calculate the number of possible cases if two variables
And if three variables ....3 variables: if one variable is x, another is y and the other two are z, the we have .... possible cases; if one variable is x, the other two are y, and the other z, then we have ....possible cases.
And the generalization of more than three.
For example: if I have
f[a_, b_, c_, d_, e_] := a d + b e + b c d - a b c d - a b d e - b c d e + a b c d e
2 variables: if one variable is x, and the other four are y, we have five polynomials;
f[x, y, y, y, y]
f[y, x, y, y, y]
f[y, y, x, y, y]
f[y, y, y, x, y]
f[y, y, y, y, x]
Account Functions. How many function is there because order of variables is necessary
if two variables are x and the other three are y, we have $C^2 _5$ = 10 polynomials.
f[x, x, y, y, y]
f[x,y , x, y, y]
f[x, y, y, x, y]
f[x, y, y, y, x]
. . . . . . . . . . . . .
f[y, x, x, y, y]
f[y,x , y, x, y]
f[y, x, y, y, x]
.....................
f[y,y , x, x, y]
f[y, y, x, y, x]
.......................
f[y, y, y, x, x]
Is this possible?
thanks for the help.