In a jar of balls with different colours, can we find a general probability distribution of having n distinct colours with N number of balls grabbed ? Assuming that any colours have an equal chance to be selected. For example :
In a jar of balls with only one colour, then we only need to draw one ball (in order to see one colour).
In a jar of balls with 2 different colours, then on average we will probably need to draw 2 (or 3) balls.
In a jar of balls with 3 different colours, on average we will need to draw 5 (or 6) balls (to see 3 different colours observed).
In a jar of balls with 4 different colours, on average we need to draw 7 balls (to see 4 different colours observed).
In a jar of balls with 8 different colours, then on average we might need to draw 15 balls (to see 8 different colours observed)
In a jar of balls with 10 different colours, then on average we might need to draw 30 (or maybe 40) balls to see 10 different colours observed
In a jar of balls with 30 different colours, then we might need to draw an infinite number of balls to see the 30 different colours
and so on (need a very large number of draws if we have larger number of colours in the jar, to observe the balls with different colours)
So, by looking at this pattern, can we find the probability model for this kind of problem ?
Thanks..
