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.

Extended data:

Common application of binomial theorem;

Methods 1: prove the related inequality with binomial.

1, pay attention to the clever construction of binomial when using.

2. When using binomial theorem to prove the inequality of combinatorial numbers, it is usually demonstrated by using the positive or negative binomial theorem and combining with the inequality proof method.

Method 2: Use binomial theorem to prove the divisibility problem or find the remainder.

1. When using binomial theorem to solve the divisibility problem, the key is to construct binomial skillfully. The basic method is to prove that one formula can be divisible by another formula, as long as it is proved that all terms expanded by binomial theorem can be divisible by another formula.

2. When dealing with divisibility with binomial theorem, the base number is usually written as the sum or difference between divisor (or a number closely related to divisor) and a certain number, and then expanded with binomial theorem, so that only one or two items behind (or before) can be considered.

3. Note that the value range of the remainder is the remainder, b∈[0, r], and r is the divisor. After the deformation is expanded by binomial theorem, pay attention to the transformation when the remainder is negative.

References:

Baidu Encyclopedia Entry-Combination Number Formula

References:

Baidu encyclopedia entry-binomial theorem