![]() ![]() In total you will find 5 × 24 = 120 possibilities. Repeat this process again with 3 as the first digit, then 4 as the first digit and finally 5 as the first digit. The smallest is 21345, the largest is 25431 and again there are 24 possibilities. ![]() Now start again with 2 as the first digit. This in total gives 6 × 4 = 24 possibilities with 1 as the first digit. In a similar manner there are 6 more with 14 as the first 2 digits and then an additional 6 with 15 as the first 2 digits. Using an argument as above I find 6 more. ![]() Now consider the possibilities with 13 as the first two digits. So far I have listed all of the possibilities with 12 in the first two places. The next largest will have 125 in the first 3 places and they are 1253. The next largest will have 124 in the first 3 places. These are the only possibilities with 123 in the first 3 places. You can write them down in numerical order from smallest to largest. Thus you have made 5 × 4 × 3 × 2 1 = 120 choices and there are 120 possible 5 digit numbers made from 1, 2, 3, 4 and 5 if you don't allow any digit to be repeated. Hence there are 2 choices for the fourth digit and only 1 choice for the fifth digit. Now that you have chosen the first 2 digits there are 3 remaining and thus you have 3 choices for the third digit. Once you have done that there are 4 digits left so you have 4 choices for the second digit. I can show you how to write them down yourself.įirst of all how many are there? If you are going to write one of them you have 5 choices as to which digit you write down first. I would like to get a list of all the possible 5 digit combinations of the numbers 12345. ![]()
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