Problem 493

Under The Rainbow

70 colored balls are placed in an urn, 10 for each of the seven rainbow colors.

What is the expected number of distinct colors in 20 randomly picked balls?

Give your answer with nine digits after the decimal point (a.bcdefghij).

彩虹之下

在容器中装有70个球，分别染上彩虹的七种颜色，每种颜色各有10个。

从容器中随机取出20个球，这些球中不同颜色的数量的期望值是多少？

你的答案应当保留到小数点后9位小数（a.bcdefghij）。