How can I know if this problem deals about permutation or not or just simply combination, is there any key word I could find to distinguish the two from a given problem?
2006-06-26 04:37:38 · 7 answers · asked by paulo_grn14 2 in Science & Mathematics ➔ Mathematics
In all these problems you are going to pick a set of objects or perform a set of actions.
If the ordering of the outcomes makes a difference, then it's a permutation. If the ordering doesn't make a difference, then it's a combination.
Example 1: The 10 runners run a race. They give medals for the first 3 places. How many different outcomes are there?
The order of finish makes a difference, since it determines who gets which medal, so it's a permutation problem.
Answer: 10x9x8 = 720
Example 2: Three students are chosen from a class of 10 to clean after a food fight. How many ways can the group be chosen?
It doesn't matter who gets picked first, they all have to clean. Ordering doesn't make a difference, so it's a combination problem.
Answer: 10C3 = 10!/3!7! = 10x9x8/3x2x1 = 120.
2006-06-26 04:50:16 · answer #1 · answered by rt11guru 6 · 0⤊ 0⤋
A permutation is just moving things around, a combination is a different set of components. For example, the number set (1, 2, 3) and the set (2, 3, 1) are different permutations but are the same combination.
2006-06-26 04:44:18 · answer #2 · answered by ebk1974 3 · 0⤊ 0⤋
'Permutations are like combinations except that in combinations order doesn't '"matter" (in the sense that abc and cba are indistinguishable and therefore each is an instance of the same combination), whereas order does matter in permutations (abc and cba are two distinct permutations).
So if the word problem doesn't specify or imply a particular order (e.g., what are the odds of getting a royal flush in a 5-card poker deal?), it's a combination problem. Note that, in the example, a royal flush is a set of cards with an implied order of display (10,J,Q,K,A), but the order I'm referring to is the order in which the cars are dealt, which the wording does not address.
2006-06-26 04:48:01 · answer #3 · answered by kirchwey 7 · 0⤊ 0⤋
Permutation
2015-12-06 21:00:59 · answer #4 · answered by Ahmad Ahmad 1 · 0⤊ 0⤋
I think it is better if you just analyze the problem first and check if the order of the elements is important or not. Example if there are 30 contestants and you have to choose champion, first runner-up and second runner-up, then definitely the order is important and you will use permutation, but if the question is like-- a manager will get 4 representatives out of 20 employees, then the order is not important and you will use combination.
As you go through several problems you yourself will discover the key words you are comfortable with. Just Analyze! That's all!
^_^
2006-06-27 00:14:22 · answer #5 · answered by kevin! 5 · 0⤊ 0⤋
If order matters, then you use a permutation. If not, then you use a combination.
2006-06-26 04:42:58 · answer #6 · answered by blahb31 6 · 0⤊ 0⤋
a permutation deals with specifics ....two people picked for Prez & vice Prez is specific
a combination is not specific ... how many possibilities ??
if you think of outcomes ... does the result need to be general (C) or specific (P)
2006-06-26 04:49:48 · answer #7 · answered by Brian D 5 · 0⤊ 0⤋