On each turn of the knob, a gumball machine is equally likely to dispense a red, yellow, green or blue gumball, independent from turn to turn. After eight turns, what is the probability P[R2Y2C2B2] that you have received 2 red, 2 yellow, 2 green and 2 blue gumballs?

Step-by-step explanation:

Given

--- [R, Y, C and B]

Required

Since each of the 4 balls are equally likely, their probability is:

From , we have:

So, the total arrangement of the 8 balls is:

The individual probability of each ball, when put together is

Lastly:

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