4-Digit Different Digit Patterns - 4536

[DecayProduct]

Homework Statement

How many 4-digit patterns are there in which all the digits are different?

Homework Equations

10!/6! ??

The Attempt at a Solution

As shown above, I used 10!/6! and I get 5040. I get the same answer of course when I use 10x9x8x7. But my book shows the answer as 4536. What am I missing?

 

[rock.freak667]

the numbers that you want to arrange do not start with a 0

 

[DecayProduct]

the numbers that you want to arrange do not start with a 0

Gadzooks! It never crossed my mind..

 

[Jamil (2nd)]

the total number of combinations of 4 digit numbers you can get is 9^4. Now just count how many contains same digits.

 

[HallsofIvy]

Choose any of the 9 digits (1 through 9) for the first digit. That leaves 9 digits for the second (because you are now allowed to use 0), 8 for the third digit, and 7 for the fourth.