Question

Independent Probabilities: These occur when the sample space remains unchanged after each selection (e.g., if you replaced the slip after each selection so that the probability of each activity remained constant).
Dependent Probabilities: These occur when the probability of an outcome affects the probability of another (e.g., failing to replace the slip, thereby narrowing the choices).
Because the movie outing is selected first and is not replaced, the other three outings will be selected from the remaining three slips, so their selection is a function of dependent probabilities. The number of ways to arrange this for the month is 3! = 6.

Answer 1

Your reasoning is correct.

If the movie slip is drawn first and not replaced, the remaining three outings are chosen without replacement, so their order is dependent and you get 3! = 6 possible orders for those three weeks.

If you want them listed, label the remaining outings A, B, C — the six orders are:
A B C
A C B
B A C
B C A
C A B
C B A

Probability notes (optional):
- Without replacement, any specific ordered sequence of the 4 outings (e.g., Movie, A, B, C) has probability 1/4 · 1/3 · 1/2 · 1 = 1/24.
- The event “Movie first” has probability 1/4 (there are 6 sequences with movie first out of 24 total ordered sequences).
- With replacement (independent draws), there would be 4^4 = 256 ordered sequences; “movie first” would still occur with probability 1/4 (64/256).