Quandaries
and Queries 

Hi Rob, Thank you very much for this wonderful web. I am always interested to know how the for digit works. I mean, you have correctly put it that the total numbers obtain from 0000 thru 9999 are 10,000. My question is, is there any simple formula to turn this simple 4 figures of say: 1234. Is 16 the correct total combination? If so is there any formula to obtain these 16 combinations. Thanks Rob. 

Hi Rob, I am not sure exactly what you are asking. Are you are asking
This would allow the same digit to be used more than once. For example 2314, 4432, and 1211 would be allowed. If this is the queston then think about constructing such a number. Write down the first digit. You have 4 choices, 1, 2, 3 or 4. Now write down the second digit. Again you have 4 choices 1, 2, 3 or 4. Thus for the 2 digit number you have constructed so far there are 4 4 = 16 choices. Now write down the third digit. Again there ae 4 choices so the number of possible 3 digit numbers is 4 4 4. Finally there are 4 choices for the last digit so the number of possible 4 digit numbers is 4 4 4 = 256. If you are asking
then there are 4 choices for the first digit but only 3 choices for the second since you can't repeat the digit you chose for the first position. Hence, in this case there are 4 3 = 12 possible two digit numbers. For the third digit there are only 2 choices and for the last digit, one choice. Thus if you are not allowed to repeat a digit the number of possible 4 digit numbers you can construct from 1,2,3,4 is 4 3 2 1 = 24. Penny 

