- #1

- 100

- 27

- Homework Statement:
- The total number of 5 digit numbers of different digits in which the digit in the middle is the largest is ?

- Relevant Equations:
- N/A

I am scratching my head on the problem but cannot figure out what to do. I tried in the following way:-

For (

_ _ _ _ _ . The middle place is fixed means only 1 way there. For the first place 9 ways (

So total no of digits in which the digit in the middle is largest ( in this case it is

For (

**9**)_ _ _ _ _ . The middle place is fixed means only 1 way there. For the first place 9 ways (

**excluding 0**) , second place (9 ways again because 9 digits are left excluding**9 and 0**). Third place is the middle one which is**already**filled, fourth place 8 ways and last place 7 ways .So total no of digits in which the digit in the middle is largest ( in this case it is

**9**) are 9*9*1*8*7. The same method would go for other numbers. Is my method correct or am I approaching the problem incorrectly?? I cannot find the answer.