Fortune Telling Collection - Free divination - How many different currencies can 1, 5, 1 yuan make up?

How many different currencies can 1, 5, 1 yuan make up?

Analysis:

According to the meaning of the question, it is found that 1 coin can form several different currency values, two coins can form several different currency values, and three coins can form several different currency values, so the answer is obtained.

Answer:

(1) 1 Coin can be composed of three different currencies: 1, 5, 1 yuan and * * *;

(2) Two coins can be composed of different currencies: 6 cents, 1 yuan 1 minute, 1 yuan 50 cents, * * *;

(3) Three coins can be composed of different currency values: 1 Yuan 60, * * *1;

* * * The number of species that can be composed is 3+3+ 1=7 (species).

A: With three coins, 1, 5, 1 yuan, seven different currencies can be formed.

Comments:

The key to solve this problem is that when 1, 2, 3 coins can form several different currency values, they must be written down to avoid repetition or omission.

Extended data:

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).

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).

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