a.Consider a hypothetical gas of four distinguishable particles,labeled W, X, Y and Z. Assume that they are distributed betweenonly two translational quantum states of energies 2E and 4E. Howmany different configurations of this gas are there?
b.Consider a hypothetical gas of three distinguishableparticles, labeled A, B and C. Each of the particles has only threequantum states of energies 5E, 10E and 15E. How many differentconfigurations of this gas have a total energy of 30E?
c.Consider a hypothetical gas of three identical particles, eachof which has only three quantum states of energies 3E, 6E and 9E.List all the different configurations of this gas that have a totalenergy of 18E assuming that the particles are (i) identical bosonsand (ii) identical fermions.
d.Consider a hypothetical gas of four identical bosons, each ofwhich has only four quantum states of energies E, 2E, 3E and 4E.Suppose the total energy of the gas is fixed at 12E. Determine theprobability of finding all four particles in the same quantumstate.
