Say I have three balls - red, green and blue in a bag. I will choose a ball from the bag and then return it, then choose another one, etc. Say I will do this 3 times; then the possibility of me picking a certain sequence (for example RGB) is 1/3 * 1/3 * 1/3. But say I do this 4 times. What is the possibility then of running into the same sequence? The desired pick becomes one of the following: BRGB or RRGB or GRGB or RGBB or RGBG or RGBR. I can do the math for this, but what is the general equation where the number of picks is X? Say I want to pick ten balls, what is the possibility of getting RGB then?
For example if I pick four times there is a (1/3)^4 chance that I would get RGBR, but my question isn't the possibility of getting a FOUR letter sequence, rather of getting a three letter sequence in a four letter possibility. The correct answer when x = 4 is (1/3)^4 *6 = 6/81.
Am I explaining this easily? Thanks.
EDIT: Please note that there is only one trial.