# How Many 4 Number Combinations Using 1 2 3 4 And What Are They?

There are a total of 24 number combinations that can be made using just the numbers 1, 2, 3 and 4. These 24 number combinations are listed below in order of number combinations, beginning with the number 1 and finishing with number combinations that begin with the number four.

1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 1431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321.

In mathematics a combination is a way of selecting several things out of a larger group, where unlike permutations, order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, an apple, orange and pear say, there are three combinations that can be drawn from this set: An apple and a pear; an apple and an orange; or a pear and an orange.

More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient. Combinations can consider the combination of n things taken k at a time without or with repetitions. If however it was possible to have two of any one kind of fruit there would be 3 more combinations: One with two apples, one with two oranges, and one with two pears.

With large sets, it becomes necessary to use mathematics to find the number of combinations. For example, a poker hand can be described as a 5-combination (k = 5) of cards from a 52 deck of cards (n = 52). The 5 cards of the hand are all distinct, and the order of cards in the hand does not matter. There are 2,598,960 such combinations, and the chance of drawing any one hand at random is 1 / 2,598,960.
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Anonymous commented
Given the numbers 1, 2, 3, and 4 there are 4 to the power of 4 (4^4) possible combinations. 256.

1111 2111 3111 4111
1112 2112 3112 4112
1113 2113 3113 4113
1114 2114 3114 4114
1121 2121 3121 4121
1122 2122 3122 4122
1123 2123 3123 4123
1124 2124 3124 4124
1131 2131 3131 4131
1132 2132 3132 4132
1133 2133 3133 4133
1134 2134 3134 4134
1141 2141 3141 4141
1142 2142 3142 4142
1143 2143 3143 4143
1144 2144 3144 4144
1211 2211 3211 4211
1212 2212 3212 4212
1213 2213 3213 4213
1214 2214 3214 4214
1221 2221 3221 4221
1222 2222 3222 4222
1223 2223 3223 4223
1224 2224 3224 4224
1231 2231 3231 4231
1232 2232 3232 4232
1233 2233 3233 4233
1234 2234 3234 4234
1241 2241 3241 4241
1242 2242 3242 4242
1243 2243 3243 4243
1244 2244 3244 4244
1311 2311 3311 4311
1312 2312 3312 4312
1313 2313 3313 4313
1314 2314 3314 4314
1321 2321 3321 4321
1322 2322 3322 4322
1323 2323 3323 4323
1324 2324 3324 4324
1331 2331 3331 4331
1332 2332 3332 4332
1333 2333 3333 4333
1334 2334 3334 4334
1341 2341 3341 4341
1342 2342 3342 4342
1343 2343 3343 4343
1344 2344 3344 4344
1411 2411 3411 4411
1412 2412 3412 4412
1413 2413 3413 4413
1414 2414 3414 4414
1421 2421 3421 4421
1422 2422 3422 4422
1423 2423 3423 4423
1424 2424 3424 4424
1431 2431 3431 4431
1432 2432 3432 4432
1433 2433 3433 4433
1434 2434 3434 4434
1441 2441 3441 4441
1442 2442 3442 4442
1443 2443 3443 4443
1444 2444 3444 4444
1234,1243,1324,1342,1423,1432
2134,2143,2314,2341,2413,1431
3124,3142,3214,3241,3412.3421
4123,4132,4213,4231,4312,4321

24 numbers.
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Greetings:

This is the basis of all the "Pick-Four" lotteries around the country.

There are 10,000 possible combinations of the numbers one through four.  They range from 0000 to 9999.

How you arrive at the answer is rather simple.  10,000 is 10x10x10.  If you start with 10 you have 10 possible combinations of one-digit numbers 0 through 9.  Multiply by ten and you get 100.  There are 100 combinations of two-digit numbers...00 to 99.  Multiply 100 times 10 and you get 1,000 combinations of three-digit numbers 000 to 999.  Multiply by 10 again and you get 10,000 combinations.

Simple as that.

I hoped this helped.

Bernie520
Seattle, WA
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