Let G be finite group and let p be a prime dividing |G|. Let S denote the set of p-tuples of elements of G the product of whose coordinate is 1:

S={(x1,x2,x3,...,xp)|and x1*x2*x3*...*xp=1}

where x1,x2,x3... belong to G. and '*' represents the binary operation under which G is a group. Note that x1,x2,x3... need not be distinct.

PROVE THAT: S has |G|^(p-1) elements.