Subject: Combinations
Name: Melissa
Who is asking: Other
Level: Secondary
Question: Hello!
I need to find out ALL of the possible 3 digit combinations of 0 - 9. Eg: 000,001,002,003. This is going to take me VERY LONG time. Any suggestions.
Hi Melissa,
I don't think that you need to write them all out.
If what you want are all possible three digit numbers then you have 10 choices for the first digit, you have 10 choices for the 2nd digit,and you have 10 choices for the 3rd digit giving you 10x10x10 = 1000 in all.
If what you want are all possible three digit numbers with no repetition of the digits then you have 10 choices for the first digit, you have 9 choices for the 2nd digit, and you have 8 choices for the 3rd digit giving you 10x9x8 = 720 in all.
If what you actually want is what you said - combinations - that's something quite different. It is the number of ways to choose 3 of the 10 digits in which order is not important. There are 6 = 3x2x1 ways to order 3 digits in a row. Thus the number of combinations of 3 of the 10 digits is 720/6 = 120 combinations.
Hope this helps,
Penny Nom