Question

Using digits 0-9, find out how many 4 digit passcodes can be configured based on:
A) the passcode can't start with a 0, a 1 or a 2 and no digits can be repeated. (I got 3,024-is this right?)
B) The passcode must begin with an odd digit and end in an even digit (repetition OK)- I got 2,025 is this right?

Answer 1

For A), I'd get \((10-3) \times 9P3\)

Answer 2

For B) I get \(5\times 10P_r2\times 5\)

Answer 3

So for A you got: 3,528? I don't understand how to do B the way you did it.

Answer 4

\[
nP_rk = n^k
\]

Answer 5

It is just permutations with repetition.

Answer 6

So B is 2250?

Answer 7

For B I'm getting 2500

Answer 8

The reason I multiply by 5 and start and end is because there are only 5 even/odd digits.

Answer 9

I did it this way: 5*10*9*5=2250. (5*10!/(10-2)!*5)

Answer 10

Did you get 3,528 for A?

Answer 11

Yes.

Answer 12

In B, can digits 2 and 3 be the same?

Answer 13

Ok thank you- so I see you did factoring for B 5*10*10*5=2500

Answer 14

Yes repetition is ok which is what I see you did with the 10*10 part.