Question

A four-digit numeric Personal Identification Number (PIN) was recently created by its user. It is known that only odd digits were used. How many PIN codes could possibly have been made if it is known that exactly one digit was repeated (ex. 1341, or 9957)?

Answer 1

why is the solution 5C2 and not 5C1 for picking the identical numbers?

Answer 2

5*4*3*3

Answer 3

.....how does that answer my question....?

Answer 4

Since there 5 odd digits
For first number we have 5 choices
For second number we have 4 choices
For third number we have 3 choices
And for fourth digit we have 3 choices as it is repeated..... (only 3 digits are already used)

Answer 5

I guess it is 4C1*5*4*3*3

Answer 6

....that still does not answer my question.....i was asking why 5C2 and not 5C1

Answer 7

why choose 2 and not 1?

Answer 8

i mean 4C2 and not 4C1

Answer 9

why is the solution to pick the identical numbers 4C2 and not 4C1

Answer 10

nevermind... i got it

Answer 11

4C2 represented the ways of choosing the location of the identical numbers....it wasn't what i thought

Answer 12

btw, what is the final answer?

Answer 13

360

Answer 14

oh.....I forgot to divide by 2

Answer 15

As there was repetation

Answer 16

why is this solution wrong:

5C1 * 4 * 3 * 4!/2!

Answer 17

4!/2! is the number of ways to pick 2 positions? I think order does not matter, so
use a combination instead

Answer 18

I guess it should have been
5C2 * 3C1 * 4!/2! OR 5C1 * 4C2 *4!/2!

Answer 19

why 4C2

Answer 20

From remaining 4 odd numbers now we need to choose 2

Answer 21

so why is plain 4*3 wrong?

Answer 22

There u are already using permutation........

Answer 23

And u used it again 4!/2!

Answer 24

seems legit....still confusing though

Answer 25

if you use permutation...you can't use permutation again?

Answer 26

No....... u can use that...... But for same thing u used it twice so it include some repetation.