In the standard coin exchange problem were each denominations are available infinite times and we need to find the number of ways in which we can form the target value :

for a recursive function int fun(int n , int val) and the arr contains the denominations.

this is how the possible cases for the recursive calls should be .

int not_take = fun(n-1 , val)
int take = fun(n ,val - arr[n])

But before seeing the solution I thought it like this instead ( definitely wrong )

int not_take = fun(n-1 , val)
int take = fun(n ,val - arr[n] ) + fun(n-1 , val- arr[n])

I considered one more case too, where we take the coin and move to the next index . I cant find a reasoning why this is wrong logically .

Might be a stupid doubt but cant get over it just like that. Can anyone tell me why is it wrong to consider that case.

Thanks