# define X_i to be the indicator variable that the ith color is present. By linearity of expectation, the expected number of colors
# is the sum of the expected values of X_i. These variables are all symmetric, so it works out to 7 * p(color blue is present).
# So, input this into wolframalpha: 7 * (1 - (60 choose 20) / (70 choose 20))
# answer is given.