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Question from Debbie:

I would prefer to gain a perform of every the feasible 5 digit combinations the the numbers 12345. say thanks to you for any kind of help. Debbie

Hi Debbie,

I can show you just how to create them under yourself.

First of all how countless are there? If you room going to write among them you have 5 choices as to which digit you compose down first. When you have actually done that there space 4 digits left for this reason you have actually 4 options for the 2nd digit. Now that you have actually chosen the very first 2 number there room 3 remaining and thus you have 3 selections for the 3rd digit. For this reason there are 2 choices for the fourth digit and also only 1 selection for the fifth digit. For this reason you have made 5 × 4 × 3 × 2 1 = 120 choices and also there space 120 feasible 5 number numbers make from 1, 2, 3, 4 and also 5 if you don\"t allow any digit to be repeated.

You are watching: Number of combinations of 5 numbers

You deserve to write them under in numerical order from smallest to largest. The smallest is 12345 adhered to by 12354. These are the only possibilities v 123 in the an initial 3 places. The next largest will have actually 124 in the an initial 3 places. Again in number order they are 12435 and also 12453. The next biggest will have 125 in the first 3 places and they space 12534 and also 12543. So much I have provided all that the possibilities with 12 in the an initial two places. The are

12345 12354 12435 12453 12534 12543

Now consider the possibilities v 13 as the very first two digits. Using an dispute as over I discover 6 more.

13245 13254 13425 13452 13524 13542

In a comparable manner there space 6 more with 14 together the first 2 digits and then second 6 through 15 as the very first 2 digits. This in complete gives 6 × 4 = 24 possibilities v 1 as the first digit.

Now begin again v 2 as the first digit. The the smallest is 21345, the largest is 25431 and again there are 24 possibilities. Repeat this procedure again v 3 as the very first digit, then 4 as the very first digit and also finally 5 together the an initial digit. In complete you will discover 5 × 24 = 120 possibilities.

See more: Famous Soccer Players With Number 12, The Best Athletes Who Wore #12

I expect this helps,Penny

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Math main is supported by the university of Regina and The Pacific Institute for the math Sciences.