Probability of drawing balls

[know]

The box contains 20 red, 15 blue, 11 white and 5 black balls. What is the minimum number of balls that need to be drawn to make sure there are 10 balls of the same color between them?
a) 37
b) 33
c) 28
d) 20
I think the answer is 33, but is there any formula for calculating this?

 

[Deleted member 4993]

The box contains 20 red, 15 blue, 11 white and 5 black balls. What is the minimum number of balls that need to be drawn to make sure there are 10 balls of the same color between them?
a) 37
b) 33
c) 28
d) 20
I think the answer is 33, but is there any formula for calculating this?

How did you arrive at the answer of 33?

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Please share your work/thoughts about this assignment.

 

[know]

I'm not sure that is correct, but I choose: 5 black balls +9 white balls+9 blue balls+10 red balls=33 balls
But is there any formula for calculating this?

 

[pka]

but is there any formula for calculating this?

No there is no formula. It simply takes brain power.

 

[Dr.Peterson]

I'm not sure that is correct, but I choose: 5 black balls +9 white balls+9 blue balls+10 red balls=33 balls
But is there any formula for calculating this?

The way I think of it is, what would my enemy do to try to prevent me from attaining my goal of getting 10 of the same color as long as possible? He'd give me 9 each of the colors he can do that with, and 5 of the other; then with the next ball, I win.

Not really a formula, though you could make one if you had to do this every day. As pka said, it's just reasoning, and it's best not to avoid thinking.