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(c)Use simple counting arguments to prove that this cannot be the case for systems with spin-one orhigher.(d)Show that 0≤ |p| ≤1, where|p|= 1 if and only ifρcorresponds to a pure state.(e)The point at the very center of the Block sphere corresponds to the completely unpolarized mixture,wherep= 0. Because this point can be approached from arbitrarily many different directions, it canresult from mixing different orthogonal pure states in an infinite number of different ways.Write anexplicit expression for the density matrix in this case, and find at least two distinct mixtures of orthogonalpure states which result in this totally mixed state.