Under The Rainbow

Published on Saturday, 13th December 2014, 04:00 pm; Solved by 4153;
Difficulty rating: 10%

Problem 493

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

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

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