Minimum numbers of balls to be drawn

[usha]

Homework Statement

suppose in a box there are 20 red, 30 black,40 blue,and 50 white balls.what is the minimum numbers of balls to be drawn, without replacement,so that you are certain about getting 4 red, 5 black, 6 blue and 7 white balls?

Homework Equations

The Attempt at a Solution

so there are total 140 balls and i have to get 22 balls with the following configuration. i tried to use this formula..
[(40C6)(20C4)(30C5)(50C7)]/(140C22)
but i am not sure... i think this gives the probability of getting this configuration... but for minimum balls to be drawn... i don't know which formula can be used...

 

[Simon Bridge]

Forget the formulas and use your understanding.
The key is that you have to be certain of those numbers...

 

[RUber]

With 140 balls and 20 red balls, how many must you draw to be certain that you will have at least one red ball?
It is probably more than 120, since there is at least one way to pull 120 non-red balls.