Question

A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number, \(d_1d_2d_3d_4\), where \(d_i,~~i=1,2,3,4, is selected from 1,2,3,4,5,6,7,8.
How many different lock combinations are possible with such a lock?
Please, help

Answer 1

you can select first digit in 8 different ways

Answer 2

Yes,

Answer 3

With replacement?

Answer 4

yes,

Answer 5

Like can we have 1132

Answer 6

if repetition is allowed, you can select each of remaining digits in 8 ways as well

Answer 7

yes @ganeshie8
no @swissgirl

Answer 8

both should be yes
or both should be no

Answer 9

My question: Why can't we apply 8C4?
No, because swissgirl gives me the wrong answer

Answer 10

if repitition is allowed, 1132 is perfetly fine for a lock right ?

Answer 11

swissgirl gave you an example for lock combination

Answer 12

what does 8C4 represent ?

Answer 13

\(8C_4\)

Answer 14

8 choose 4

Answer 15

\(8^4 \ne 8C4\)

Answer 16

8C4 represents number of ways of choosing 4 "different" things from a set of 8 "different" things

Answer 17

we can use "8C4" for forming different subsets of size "4"

Answer 18

C in 8C4 literally means "choose/pick"

Answer 19

I got you, thank you.
One more question: This question is about how many sample space I can have, right?

Answer 20

what is a sample space exactly ? il need to google

Answer 21

and 8^4 = 4096
How can you guys get 1132?

Answer 22

1132 was just an example of key combination

Answer 23

she was asking if repetition is allowed or not

Answer 24

notice that in `1132` ,
`1 ` is repeated two times

Answer 25

it was a question asked to clarify your question

Answer 26

ohoooh... that's an example of the combination. I am sorry for misunderstanding. @swissgirl
Thank you you both.

Answer 27

Lol Thats alright .... :D