Quandaries
and Queries 

Today I was aked a question by my geometry teacher. It was, what is the sum of all the possible combinations of the numbers 1, 2, 3, 4, 5, and 6. He said all the possible combinations were 720. I would like to know how u could do this, and what the answer is. Thank You, Kyle, 9th grader 

Hi Kyle,
I think that your teacher is looking for the number of arrangements you can make with the digits 1,2,3,4,5 and 6. For example 145236, 462351,... I think of having six positions and I am going to build a six digit number from the digits 1,2,3,4,5 and 6 without repeating a digit.
Start with the left most position. You have 6 choices of what digit to put in that position. Thus you can build 6, one digit numbers. Each of these 6, one digit numbers can turned into a two digit number by placing one of the 5 remaining digits in the second place. Thus there are 65=30, two digit numbers you can construct. Simularly, each of the 30, two digit numbers can be turned into a three digit number by placing one of the 4 remaining digits in the third place. Can you see now how you get 720, six digit numbers? Penny 

