Today finally know how this equation comes from.
If you pick n objects from N objects (with replacement, ordering doesn't matter), then the equation will be like:
n+(N-1)/(N-1)
you can image that the n objects divided in to N groups, and since you want to make N divisions, then how many bars you need to have to compete them, the answer is N-1, like you need to 2 bars to divide a line of objects into 3 groups.
Then you count (N-1) bars in, you will have n + (N-1) objects, then you want to know how many ways you can have to pick n objects from N objects which also are the same as how many ways you can put N-1 bars to n objects to divide them into groups.
Awesome, you got it, you just have to think about it more little, and more detailed, then you will clear the mist, go Wallace Tiger, just put a smile and you will be fine : )
