1. ## Multiplication Rule

A PIN is a sequence of any 4 digits (repetitions allowed). How many different PINs are possible?

Ans:
10,000 PINs are possible

2. Originally Posted by nikk
A PIN is a sequence of any 4 digits (repetitions allowed). How many different PINs are possible?

Ans: 10,000 PINs are possible
Think about each digit of the PIN individually, how many numbers can there possibly be?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10 possibilities

Say the first digit is a 0, move on to the second digit, this digit can, again, have 10 possibilities.

So for each possibility of the first digit, there are another 10 possibilites for the second digit. This would correspond to: 10 x 10 in terms of math.

Then there would be another ten possibilities for the third digit of the PIN, and the same for the fourth digit of the PIN.

In total, you would have: 10 x 10 x 10 x 10 = 10,000 possibilities.

This is true when you're trying to figure out the number of possibilites of anything else where repetition is allowed. If there are n number of possibilities for m spots (in this case 10 possibilities for 4 spots), then the answer would be $\displaystyle n^m$ possibilities.

3. Originally Posted by star_tenshi
Think about each digit of the PIN individually, how many numbers can there possibly be?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10 possibilities

Say the first digit is a 0, move on to the second digit, this digit can, again, have 10 possibilities.

So for each possibility of the first digit, there are another 10 possibilites for the second digit. This would correspond to: 10 x 10 in terms of math.

Then there would be another ten possibilities for the third digit of the PIN, and the same for the fourth digit of the PIN.

In total, you would have: 10 x 10 x 10 x 10 = 10,000 possibilities.

This is true when you're trying to figure out the number of possibilites of anything else where repetition is allowed. If there are n number of possibilities for m spots (in this case 10 possibilities for 4 spots), then the answer would be $\displaystyle n^m$ possibilities.
if repetitions not allowed, what is the ans? thank for good information & explanation

4. use $\displaystyle ^nC_r$

$\displaystyle ^{10}C_4$

= 210

5. Originally Posted by Kevlar
use $\displaystyle ^nC_r$

$\displaystyle ^{10}C_4$

= 210
Actually you use $\displaystyle ^nP_r$ since the order is important:

$\displaystyle ^{10}P_4$