Probability Math Question? Help!?

Question

A bag contains 500 beads, each of the same size, but in 5 different colors. There are 100 beads of each color and I am blindfolded What is the fewest number of beds I must pick to be absolutely sure there are 5 beads of the same color among the beads I have picked?

I don't understand how to solve these kinds of problems. I thought the answer was 20 (I took a guess), but on the answer sheet, it said the answer was 21. Why is it 21? How did you solve it?

Answer 1

I don't know

How is it twenty one? What if you're unlucky and pick 100 beads of the same color first?..

Answer 2

If you have 20, you could end up with 4+4+4+4+4.

But with 21, the extra one must be one of the 5 colors. So 21 is the answer.

Answer 3

Think about it like this:  

What is the maximum number of beads you can pick without having 5 of the same color?  Well, 4 of each color, 5 different colors so 20.

21 is 1 more than that =)