Was going through unofficial sat probability questions and I was wondering something. How do you know what to count as a combination and what to count as a permutation? For example, one question was asking for the total number of ways to roll a seven on a pair of dice. Some could say that 5,2 is unique from 2,5 while others may say that they are identical. What would the SAT expect as an answer and would they give any hints to suggest such an answer? Any response would be greatly appreciated!
The SAT does not directly test combinations & permutations.
@KonRaim The main difference is whether the order of which you are selecting your objects matters.
A well-written question should be clear and unambiguous. If the two dice are treated as distinct, then (5,2) is different from (2,5). However, I wouldn’t consider this a “combination” or “permutation” question since you are not actually choosing items from a set.
Here is an example where the difference between a combination and a permutation (I sometimes avoid using “permutation” since it has a different meaning within combinatorics) becomes more apparent:
Combination:
Q: How many ways can I select a 3-person committee from a group of 10? (note that ABC is the same as ACB, CAB etc.)
Permutation:
Q: How many ways can I select the president, vice president, and treasurer from a group of 10? (ABC is not the same as ACB, CAB)
Thanks, MITer. Informative and well-written!