I am looking for a way to define anticummuting numbers (variables) in mathematica. Let say we have a set of four variables like $ {x_1,x_2,x_3,x_4}$ which I need to get all possible permutation of them then multiply to appear as a sum as $ $ x_1*x_2*x_3*x_4+x_1*x_2*x_4*x_3+(22\,{\rm terms})$ $ but here as we said these variables are Grassmann so whenever we interchange any two of them we should get a negative sign, i.e $ x_1*x_2=-x_2*x_1$ , for example the above expression should appear as $ $ x_1*x_2*x_3*x_4-x_1*x_2*x_4*x_3+(22\,{\rm terms})$ $

I know how to permute the variables and convert them to have a some over all 24 possible permutations, but I do not know how get their signs correctly…any idea?