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# How many 3 number combinations can you make from 1 2 3 4 5 using each number once?

Updated: 12/20/2022

Wiki User

13y ago

123, 124, 125, 132, 134, 135, 142, 143, 145, 152, 153, 154

213, 214, 215, 231, 234, 235, 241, 243, 245, 251, 253, 254

312, 314, 315, 321, 324, 325, 341, 342, 345, 351, 352, 354

412, 413, 415, 421, 423, 425, 431, 432, 435, 451, 452, 453

512, 513, 514, 521, 523, 524, 531, 532, 534, 541, 542, 543

A total of sixty combinations.

You could also use the Permutation formula with no repetition to get the result, without having to list them all out. This is important once you start getting into higher numbers.

The formula is n! / (n-r)! where n is the total number of items, and r is the number of items you are taking for each permutation.

The exclamation (!) means factorial. You take n * (n-1) * (n-2) * (n-3) * . . . . * 1.

In this case n=5 and r=3

so 5! / (5-3)! = (5 * 4 * 3 * 2 * 1) / (2 * 1) = 120/2 = 60. I'm posting a link for more information.

Wiki User

13y ago