w i , BE = ( n i + g i − − 1 ) ! n i ! ( g i − − 1 ) ! = C n i n i + g i − − 1 , where C k m is the k -combination of a set with m elements. The total number of arrangements in an ensemble of bosons is simply the product of the binomial coefficients C n i n i + g i − − 1 above over all the energy levels, i.e. W BE = ∏ ∏ i w i , BE = ∏ ∏ i ( n i + g i − − 1 ) ! ( g i − − 1 ) ! n i ! ,