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Write a function to compute the number of combinations that

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Reference no: EM131416724

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin. 

Note: You can assume that 

0 <= amount <= 5000 
1 <= coin <= 5000 
the number of coins is less than 500 
the answer is guaranteed to fit into signed 32-bit integer 

Example 1: 

Input: amount = 5, coins = [1, 2, 5] 
Output: 4 
Explanation: there are four ways to make up the amount: 
5=5 
5=2+2+1 
5=2+1+1+1 
5=1+1+1+1+1 
Example 2: 

Input: amount = 3, coins = [2] 
Output: 0 
Explanation: the amount of 3 cannot be made up just with coins of 2.

Reference no: EM131416724

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