### Permutation Problem Explanation**Problem Statement:**For the following system, what is the number of permutations with occupation numbers \( N_1=1 \), \( N_2=2 \), \( N_3=1 \), and \( N_4=0 \)?**Energy Levels:**- \( E_4 = 3\varepsilon \)- \( E_3 = 2\varepsilon \)- \( E_2 = \varepsilon \)- \( E_1 = 0 \)**Multiple Choice Options:**- \( a. \) 4- \( b. \) 6- \( c. \) 8- \( d. \) 12- \( e. \) 24**Explanation:**This problem involves finding the number of permutations in a system where particles are distributed across different energy levels. The occupation numbers given (i.e., \( N_1, N_2, N_3, N_4 \)) indicate how many particles occupy each energy level. The task is to determine the number of ways these particles can be arranged according to the given occupation numbers.

The number of permutations can be calculated by using N(P) = ∑NiEi Here Ni is the occupation number…

Answered: For the following system, what is the…

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