## anonymous 4 years ago How many possible three-digit passwords can be formed using digits 0 through 9 if digits are repeated? 30 , 720 , 1,000

1. amistre64

10 options for the 1st number 10 options each for those 10; 10*10 and 10 options each for those: 10*10*10

2. anonymous

which is the same as asking "how many three digit numbers are there?"

3. LollyLau

what do you mean by "digits are repeated"?

4. amistre64

000 to 999

5. LollyLau

does that mean that at least two of them must be the same?

6. anonymous

idk its on my math test

7. LollyLau

-.-

8. LollyLau

9. amistre64

lol, i hate interpreting word problems

10. amistre64

do digits have to be repeated? or CAN they be repeated?

11. anonymous

no , she doesnt even know

12. LollyLau

how can she don't know???????

13. amistre64

most likely I would say it means that the option is left open that they CAN be repeated, but is not a requirement

14. anonymous

bc shes dumb like that , its an online class & shes not even a math teacher

15. LollyLau

but its given =.=

16. amistre64

17. anonymous

lol

18. anonymous

Here is a good way to think of such things, I find...Let some arbitrary password be $x_1x_2x_3$ (where we mean digits next to each other, not multiplication). So we have $x_1,x_2,x_3 \in \{0,1,2,...,9\}$Now, each position has the choice of 10 digits, 0 through 9 inclusive. So the answer is 10x10x10 = 10^3 = 1000.

19. anonymous

If the password was n digits long, then the number of possible choices is $10^n$

20. anonymous

amistre64 has a good way of thinking about it, since your first digit has 10 options, and for each of those first digits there are 10 options for your second digit. So there are 10*10=100 options for two digits. Now for each of those 100 options, there are 10 options for your third digit. So for any three digits, there are 100*10 options.

21. anonymous

logically speaking... 3 digit password starts from 000 to 999.... now u can count how many of them are between 000 & 999 inclusive. It will include all possible repeating numbers.