You are watching: How many ways can you arrange 4 things

Subject: number combination Who are you: other (All) I have 4 numbers and also want to find all possible combinations. I come up v 24 but that seems too small...am ns correct that there should be more? Thanks, Candace |

Hi Candace. Let"s contact the four numbers a, b, c, and d. a, b is one combination, and a, b, c, d is another. We can list them all out, however let"s approach this in a more systematic way. We have four original numbers, so any given mix Q may have actually from 0 come 4 of these numbers in it. How numerous ways are there of choosing zero items indigenous a group of four? just one. How numerous ways room there of choosing one item from a group of four? count them out: a, b, c, d - that"s four. How plenty of ways are there of picking two items indigenous a team of four? an initial we pick one (four choices), climate select one more (from the staying three, therefore that"s three choices). But if we choose a and then b, that is the same as selecting b and also then a, for this reason we division by two to eliminate the duplicates. 4x3/2 = 6. Now let"s look ago at what we"ve done. When we selected items for our combinations, we separated the group into 2 parts: one that is selected and also one that is not. Because that every combination we selected, the remainder is another mix of the initial four. So as soon as we discovered that there is just one way of picking zero items, us are likewise saying that there is simply one mix with all 4 items (that makes sense). It also way that once we selected one article (four choices), we produced four different combinations with three items. Now us know all of the combinations and can include them up: 1 + 4 + 6 + 1 + 4 = 16 various possibilities. ---- A connected topic to combine is "permutations". As soon as order matters, you usage permutations because combinations think about order come be irrelevant ( a, b is the same as b, a). If you meant to speak "permutations", climate you are most likely asking the concern "how numerous different ways can I arrange the stimulate of 4 numbers?" The answer to this inquiry (which you obtained right) is 24. Here"s how to watch this: 1. Pick among the four numbers (there space four choices in this step). 2. Pick among the remaining three numbers (there space three choices). 3. Pick among the continuing to be two numbers (two choices) 4. Pole the critical number on the end. You multiply these options together to obtain your result: 4 x 3 x 2 (x 1) = 24. Combinations and also permutations are often perplexed by students - they room related, yet they mean various things and can command to completely different interpretations of situations and also questions. It doesn"t help that "combination locks" are really "permutation locks" because order absolutely matters! |