Given infinite coins of some currency of denominations : 1,2,5,10, so In how many unique distinct ways can we obtain a total amount of say: 25 ? Same thing how to do it for non-unique repeated combinations or permutations allowed ?

Question

Accepted Answer

There are multiple ways to obtain a total amount of 25 using coins of denominations 1, 2, 5, and 10. The question asks for unique distinct ways and non-unique repeated combinations or permutations.

For unique distinct ways, you can use dynamic programming to calculate the number of ways to reach the target amount.
For non-unique repeated combinations or permutations, you can use a recursive function to generate all possible combinations.
Example for unique distinct ways: [1, 2, 5, 10] can be used to make 25 in 4 unique ways.
Example for non-unique repeated combinations: [1, 2, 5, 10] can be used to make 25 in multiple non-unique ways.

Given infinite coins of some currency of denominations : 1,2,5,10, so In how many unique distinct ways can we obtain a total amount of say: 25 ? Same thing how to do it for non-unique repeated combinations or permutations allowed ?

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