It is known that Xiaohong 5 yuan has 1 RMB, 2 yuan has 3 RMB and 1 RMB has 6 RMB. The specific analysis is as follows:

1.5 yuan only has 1 piece, so the payment method including 5 yuan is only1:5+1;

2. It is known that there are three 2 yuan, and there are three payment methods including 2 yuan: 2+2+2+1,2+1+1+0+1;

3. There are 6 known 1 yuan, of which 1 yuan. There are four payment methods:1+1+65438+1+65438+1.

So Xiaohong bought a pencil case in 6 yuan by 1+3+ 1=5 payment methods.

Extended data:

In mathematical operation, combination is to take any m(m≤n) elements from n different elements to form a group, which is called the combination of m elements of 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).

Calculation formula:

C(n，m)=C(n，n-m).(n≥m)

Other permutation and combination formulas take out the cyclic permutation number of m elements from n elements =A(n, m)/m=n! /m(n-m)！ . N elements are divided into K classes, and the number of each class is n 1, n2, ... nk. The total number of permutations of these n elements is n! /(n 1！ ×n2！ ×...×nk！ ). K-class elements, the number of each class is infinite, and the combined number of M elements extracted from them is C(m+k- 1, m).