Question

There is a bag we 12 pieces of candy; 1 blue, 1 yellow, 3 brown, 3, green, 2 red, 2 orange. Someone pours them out in a line...

Whats the prob that colors remain together in line? What if 1million people did this same task -- what the expected number of people who will have colors in line?

Answer 1

Let's find out the number of ways in which the colors remain together in one line. Treat the balls with the same color as one unit. Hence, we have 6 units (or 6 colors) of balls in a line.

Note an important assumption: The balls of the same color are not distinct.

The balls can be arranged in 6! ways. These are the number of ways in which the colors remain together in the line.

Total number of ways in which the balls can be arranged = 12!

Probability that colors remain together = 6!/12! = 1.503 x 10^-6

b) If 1 million people or 10⁶ people perform the task, expected number of people who will have colors in line are:

P(X)*10⁶ = 1.503 x 10^-6 x 10⁶ = 1.5 people