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4! = 4*3*2*1 = 24
Technically speaking, there are 24 permutations because that is the correct math term when the order matters. Meaning, 1258 is no the same as 1285.
In English we commonly use the word "combination" loosely, without thinking if the order of things is important. In math we should be precise. If the order matters, we should call it a permutation. Along those lines, the locks that we commonly call combination locks would really be called permutation locks. That is why I say we use the term loosely.
So a permutation is an ordered combination.
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What is the sum of all possible four digit numbers using the digits 2518?
Some 24 different numbers summing to 107,357 is the result. (A non-replacement set was used; you can't use a number more than once, so no "5555" or "5512" or the like.) 1258, 1285, 1528, 1582, 1825, 1852 2158, 2185, 2518, 1581, ... 5128, 5182, ... 8125, ...
What is every combination of a 4-digit number using the numbers 1234567890?
There are 210 of them and they are:0123, 0124, 0125, 0126, 0127, 0128, 0129, 0134, 0135, 0136,0137, 0138, 0139, 0145, 0146, 0147, 0148, 0149, 0156, 0157,0158, 0159, 0167, 0168, 0169, 0178, 0179, 0189, 0234, 0235,0236, 0237, 0238, 0239, 0245, 0246, 0247, 0248, 0249, 0256,0257, 0258, 0259, 0267, 0268, 0269, 0278, 0279, 0289, 0345,0346. 0347, 0348, 0349, 0356, 0357, 0358, 0359, 0367 ,0368,0369, 0378, 0379, 0389, 0456, 0457, 0458, 0459, 0467, 0468,0469, 0478, 0479, 0489, 0567, 0568, 0569, 0578, 0579, 0589,0678, 0679, 0689, 0789, 1234, 1235, 1236, 1237, 1238, 1239,1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267,1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349,1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389,1456, 1457, 1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489,1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789,2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367,2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467,2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579,2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467,3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579,3589, 3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579,4589, 4678, 4679, 4689, 4789, 5678 ,5679, 5689, 5789 and 6789.
