# A few solutions of bijective proof problems

Difficulty:

[1] easy

[2] moderately difficult

[3] difficult

[u] unsolved

[?] The result of the problem is known, but I am uncertain whether a combinatorial proof is known.

[∗] A combinatorial proof of the problem is not known. In all cases, the result of the problem is known.

## 1.Elementary Combinatorics

### 1.[1]

PROBLEM: The number of subsets of an

## proof

PROOF: A way of choosing element can be described as a binary number, and the number of ways is

### 2.[1]

PROBLEM: A composition of

## proof

PROOF: Using “Stars and bars” method, there will be some bars to divide

### 3.[2]

PROBLEM: The total number of parts of all compositions of

## proof

PROOF: I consider that using power series is extremely easy, but we can’t use it…

Still using “Stars and bars” method, we consider that a bar in