Question

Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible?
34
40
5,040
10,000

Answer 1

ok, this one would be like if you had four spinners, each one with numbers 1 - 9 on them.

Answer 2

When dealing with a larger amount of outcomes and when counting the number of possibilities, you would multiply.

Answer 3

k

Answer 4

*0 - 9

Answer 5

So what is the largest code they can make?

Answer 6

um.....D

Answer 7

I mean what numbers are the largest in the 4-digit code?

Answer 8

her largest possibility.

Answer 9

C

Answer 10

9876

Answer 11

k

Answer 12

so it has to match?

Answer 13

no

Answer 14

ok?

Answer 15

so, do you know how to calculate the probability?

Answer 16

no

Answer 17

\[\frac{ n! }{ n-r! }\]

Answer 18

So n is the amount of numbers
r is the total numbers needed

Answer 19

You could do it using the method @Aqual described or apply permutations

She has to choose 4 digits from 10 total, and order matters. This equates to \(\text{nPr(10,4)}\). Nothing else needed at this point. Just calculate it using the formula for permutations

Answer 20

Oh wait sorry I interrupted you @Aqual, I didn't see you were explaining with permutations too. You can carry on.

Answer 21

im back

Answer 22

ill try to finish

Answer 23

k

Answer 24

back

Answer 25

k

Answer 26

so if you filled it in, it would look like \[\frac{ 10! }{ 10 - 4! }\]

Answer 27

so 6?

Answer 28

no

Answer 29

the factorial affects it

Answer 30

k

Answer 31

do you know what a factorial is?

Answer 32

yes

Answer 33

so I have to divide

Answer 34

So 5,040