Question

Social Security: Find the number of possible 9-digit social security numbers if the digits may be repeated.

Answer 1

yay sumone'shere to help me!

Answer 2

We have nine digits in a number. For each digit, we can have any number 0-9. That is a total of 10 possible numbers per digit.

[1][2][3][4][5][6][7][8][9]
^ ^ ^ ^ ^ ^ ^ ^ ^
[each is a # 0-9]

Looking at smaller examples to help us with the bigger picture, if we only had two digits, we could have...
10 10 more 10 more annnd this is the last 10, 10 10's.
00, 01, 02, .. 09; 10, 11, 12, ..., 19; 20, 21, 22, ..., ; 90, 91, 92, ... 99.
So, 10*10, or 10^2 possible numbers. Similarly, when we have 9 digits, it would be 10*10*10*...*10, 9 times, or 10^9 possible numbers.

Answer 3

aah, that didn't line up as nicely as I wanted it! D:

Answer 4

i don't get the the 10...10 more...and 10 more annnd...

Answer 5

yeah, I meant to put it over each group of 10 numbers
00, 01, 02, 03, 04, 05, 06, 07, 08, 09 (I00-09)
10 numbers here
10, 11, 12, 13, 14, 15, 16, 17, 18, 19 (10-19)
and 10 more here
20-29 is 10 more
30-39 is 10 more possible numbers
40-49, 50-59, 60-69, 70-79, 80-89, 90-99; that's 60 more. In total we have 100 numbers for 2 digits with 10 possible numbers per digit, so 10^2 = 100

just trying to give you an idea of why its 10^2 for 2 digits and 10^9 for 9. :)

Answer 6

Perhaps if you look at like this: Imagine if Social Security Numbers were only 1 digit: you'd have only 10 possible SSN's. Now if SSN's were 2 digits, you'd have the digits [0 to 9] for the first part of the SSN, then [0 to 9] for the second part

So 1 Digit SSN --> [0 to 9] means 10 possible numbers or 10^1 SSNs
So 2 Digit SSN --> {0 to 9] and [0 to 9]. means we actually have 10^2 possible SSNS.

We have 100 possible SSN for 2 digits because for each First Digit then have 10 options for the Second Digit if repetition is allowed.

Answer 7

So, can you see how this works up to 9 digit SSNs?

Answer 8

so the answer's 100?

Answer 9

how did you get that?

Answer 10

nvm..is it 3628800?

Answer 11

if you have 9 digits for an SSN... __ __ __ __ __ __ __ __ __ are blanks you need to fill in with numbers from [0 to 9]

Answer 12

who did you get 3628800?

Answer 13

10*9*8*7*6*5*4*3*2*1=3,628,800

Answer 14

that is 10 factorial

Answer 15

10!

Answer 16

What you actually determined was the number of SSN's if you could not repeat numbers in each blank...

Answer 17

but you are allowed to repeat numbers here

Answer 18

ya, dat's da part i don't really get..how to solve..it.... D:

Answer 19

is it 10*10*10*10*10*10*10*10*10*10?

Answer 20

10,000,000,000?

Answer 21

that'd be if you had 10 digits, but we only have 9 digits

Answer 22

ah, interesting, that's it

Answer 23

heh, right concept, but AccessDenied is right,

Answer 24

hmmm.... 9*9*9*9*9*9*9*9*9?

Answer 25

No, he meant that you did 10^10, which would be right if you have to make 10 digit SSNs

Answer 26

but you must only make 9-digit SSNs, like 670-43-2333 could be one. that would mean you have ([0 to 9] [0 to 9] [0 to 9]) - ([0 to 9] [0 to 9]) - ([0 to 9] [0 to 9] [0 to 9] [0 to 9])

Answer 27

the - is just for grouping, it's not subtractin

Answer 28

? i don't get ur point here... D: ?

Answer 29

Perhaps if you look at like this: Imagine if Social Security Numbers were only 1 digit: you'd have only 10 possible SSN's. Now if SSN's were 2 digits, you'd have the digits [0 to 9] for the first part of the SSN, then [0 to 9] for the second part

So 1 Digit SSN --> [0 to 9] means 10 possible numbers or 10^1 SSNs
So 2 Digit SSN --> {0 to 9] and [0 to 9]. means we actually have 10^2 possible SSNS.

We have 100 possible SSN for 2 digits because for each First Digit then have 10 options for the Second Digit if repetition is allowed.

Answer 30

can you tell me how many 3 digit SSNs you can create?

Answer 31

with repetition?

Answer 32

1000?

Answer 33

how did you get that?

Answer 34

10*10*10...i think?

Answer 35

why did you do that?

Answer 36

..bcuz then u can repeat it and so u always keep the 10 and since it's 3 digits, u hafta multiply the 10 3 times?

Answer 37

Yes, you can repeat, and yes, when you add another digit you then have 10 more numbers to match with the previous 100 combinations you created with 2 digit SSNs

Answer 38

Basically, what you are doing in this problem is just a lot of counting. And you are learning more advanced ways to count here ;)

Answer 39

the answer's 100? rite?

Answer 40

the is the answer to what?

Answer 41

wut?

Answer 42

lilai3 This is the asker
the answer's 100? rite?

Answer 43

So you said 10^3 for 3-digit SSns

Answer 44

so 100 is rite... -__-

Answer 45

Sorry, I'm confused with what you are saying 100 is the answer to.

Answer 46

nvm.....i don't no how ur suppose 2 do dis....how many digits r there nayways?

Answer 47

OK

Answer 48

So you have the numbers 0, 1,2,3,4,5,6,8,9 those are the basic units we'll be working with

Answer 49

if you want to make the number "23". You will use the numbers "2" and "3' from our basic building units. So, in order to count higher than 9, we have to repeat numbers

Answer 50

0,1,2,3,4,56,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21...

Answer 51

but it doesn't give you how many digits there r...?

Answer 52

So assume you can use all the basic numbers (0 to 9)

Answer 53

k?

Answer 54

OK, so in order to count to 10, we have to introduce repetition of numbers

Answer 55

11

Answer 56

mmmhhmmmm

Answer 57

so you have two blanks __ __ . the first blank is for the more tens units and the second blank is for the ones units

Answer 58

so the value 23 actually is 20 +3 which actually is 2 * 10 + 3

Answer 59

but the problem i'm saying is...u don't no how much digits there r...if it's 2 or 3 of 4

Answer 60

Do you mean you are unsure if you can use all of numbers 0,1,2,3,4,5,6,7,8,9?

Answer 61

or just a few of them?

Answer 62

my point is...that well, the problem doesn't give you how many social security number digits there are.. if its a 2-digit like 23, or a 3-digit, like 265...u no?

Answer 63

The problem states you will make a 9-digit SSN, this would mean you can an SSN with that looks like 000,000,000 all the way up to 999,999,999

Answer 64

so then how come ur only doing the 2digits?

Answer 65

I'm trying to make the concept simpler to show how you do for a simpler problem, then gradually make the problem more complex, up to 9 digits in this case

Answer 66

o..never mind then....my bad... but *sigh* this is...complicated..to me.... D:

Answer 67

No problem. That's why I thought we should start simpler.

Answer 68

OK. Here is a new problem: If you want to make a 1-digit SSN, how many could you make using the numbers {0 to 9} ?

Answer 69

We will gradually work through this complexity until you can solve your question ;)

Answer 70

ok

Answer 71

So, can you answer my new question?

Answer 72

like, um, 9?

Answer 73

10

Answer 74

almost, you have the numbers 0, 1,2,3,4,5,6,8,9

Answer 75

Yes, 10 is correct

Answer 76

Now, how many 2-digit SSns can you create?

Answer 77

remember, that would making the numbers, 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11 ...up to 99

Answer 78

mmmm....uh....20, perhaps? i'm not really sure.

Answer 79

well, how many numbers are the from 00 to 99?

Answer 80

100

Answer 81

Exactly

Answer 82

So, what is an easy way to count the numbers? Here is another idea: if you have 4 groups fo 5 laptops, how many laptops do you have total?

Answer 83

so if we're at the 9-digit , then that means there's 1,000,000,000 possilibities, rite?

Answer 84

sorry..didn't c ur question...at first.. i wuz busy typing.. sorry

Answer 85

Yes, you are right 1,000,000,000 possibilities

Answer 86

for 9-digit SSns

Answer 87

um...so dat's it.. dat's da answer?

Answer 88

Yes, how did you get that?

Answer 89

easy, then. if 2 digits, 2 zeros.. and also, 10 to the power of 9... 10*10*10*10*10*10*10*10*10

Answer 90

Cool, so how many would there be fore a 10-digit SSn?

Answer 91

10,000,000,000

Answer 92

Solid, 10^10

Answer 93

Do you think you've got it now?

Answer 94

YES.. TOTALLY.. NOW.. DAT WUZ SOOO EASY*ROLLS EYES* HOW COME I DIDN'T UNDERSTAND U B4?

Answer 95

thx for ur help! i gr8ly appreciate it!

Answer 96

hehe, well, learning new concepts seems obvious when you've learned them ;)

Answer 97

-__- u could've just told me... -__-

Answer 98

You mean just given you the answer?