So I am very confused about when to use combinations and permutations in questions that ask me to find the amount of ways something can be ordered.
For example, I was trying to answer a question that asked to find get $5$ kinds of cards (aces, twos, threes, etc) in a $5$ card hand. I thought that this would be a permutation $P(13,5)C(4,1)^5$, since I had read that the ways to get a full house ($2$ of one type and $3$ of another) was $P(13,2)C(4,3)C(4,2)$, and thought it would work the same way for this problem, but it ended up being a combination of $C(13,5)C(4,1)^5$.
Why is this the case? And how can I identify when to use combination or permutation?
Thanks,
Kyle
Best Answer
If the order of the objects or the cards matters you need to use permutation.
If the order of the objects doesn't matter, you need to use combination.
In your example, any of the five cards can be picked randomly, where the order does not matter, so you use combination.
Hope this helps.