N balls are put in two different boxes, and the boxes can be empty.

If we discuss balls, there are two choices for each ball, and * * * has 2 n placement methods.

According to the principle of classification, box 1 has cn0 ways of not releasing balls, cn 1 planting one ball, cn2 planting two balls, cnn planting n balls, and cn0+cn 1+cn2+…+cnn planting n balls. Obviously, the results of the two methods are the same.

Definition of arrangement:

From n different elements, any M (m ≤ n, m and n are natural numbers, the same below) elements are arranged in a column in a certain order, which is called the arrangement of taking out m elements from n different elements; All permutation numbers of m(m≤n) elements taken from n different elements are called permutation numbers of m elements taken from n different elements, which are represented by symbol A(n, m).

Calculation formula:

Besides, the rule is 0! = 1(n！ It means n(n- 1)(n-2)... 1, which is 6! =6x5x4x3x2x 1 .

Definition of combination: taking any m(m≤n) elements from n different elements and combining them into a group is called taking m elements from n different elements; The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements. Represented by the symbol C(n, m).