Question 821432: In how many ways an ATM pin number can be arranged so that the 2nd and 3rd digits are never the same? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! You have 10 choices for the second digit and for each of those choices, you would have 9 different digits to choose the third digit from.
That gives you permutations made with 2 different digits.
Another way of getting to the same result, would be counting how many 2 digit permutations there are, and subtracting the ones that have the same digit repeated (100, to get .
For each of the 90 permutations found for the two middle digits, you can choose the first and last digits any way you want, so you have 10 choices for each.
Those choices multiply and the total number of ways an ATM pin number can be arranged so that the 2nd and 3rd digits are never the same is
