Intrinsic probability in correct Boltzmann counting 
Why $\lambda_i$ can be set to unity? What it means?
That picture comes from Huang's book.
 A: The quantities $\lambda_{i}$ (or $g_{i}$ as they are known in the second edition of Kerson Huang's Statistical Mechanics) have two roles.  On one hand, they represent a coarse-graining of the micro-states of the system.  The $i$th box described in the text is not just a single state but a (large) number of states that are combined together to make a cell.  This is reasonable if the single-particle states making up the cell are still similar enough to be effectively indistinguishable macroscopically.  This is depicted in Fig. 8.1 on page 181 of the second edition.
Using these coarse-grained cells (where each cell can contain a large number of particles) simplifies the mathematics of state counting.  However, the analysis can be done without this coarse-graining.  This brings up the second reason why the quantities $\lambda_{i}$ (or $g_{i}$) are used.  Many expectation values are most easily calculated as derivatives of the partition function with respect to one or more $\lambda_{i}$.  This is shown in section 9.1 (second edition again), where fluctuations in the energy are calculated via the action of powers of $g_{i}\frac{\partial}{\partial g_{i}}$.
