Should the sample space of an experiment include all the outcomes irrespective of their order. For example-
A box contains 1 red and 3 identical white balls. Two balls are drawn at random from the box in succession without replacement.
The sample space given in the textbook is WR,RW,WW But according to me the sample space should be RW1,RW2,RW3,W1R,W2R,W3R,W1W2, W1W3,W2W3
How should one decide what to use in which situation as the same book uses my method in many other questions. For example, another question says-
A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. All discs are similar in shape and size. A disc is drawn at random from the bag
The sample space given in the solution is- R1,R2,R3,R4,B1,B2,B3,Y1,Y2
What is the real logic to be used while describing the sample space?
The first experiment has two trials, and each two-letter experiment outcome is meant to express in sequence the two trial outcomes. Since the white balls are identical, your proposed outcomes $RW_1, RW_2$ and $RW_3$ are indistinguishable, so are collectively effectively just the single outcome $RW.$
The second experiment has one trial, and here the exercise apparently considers the four red balls to be non-identical, i.e., $R_1,R_2,R_3,R_4$ to be distinct outcomes.