4digits28thmm

[nuthan]

A 4-digits number is consists the numbers selected from 0 to 9 (the numbers should can be used repeatedly, not sure). The number is greater than 1000; the hundreds digit is 0 or 1 and when is 0, the tens' digit cannot be 0. How many such numbers are possible?

 

 

9*2*9*10

 

[Jai Gurudev]

IMO,

 

For the thousands number the choice set is {1-9} = 9choices

For Hundreds digit:{0-1} = 2 choices

For Tenths digit :{1-9 or 0 -9} based on Hundreds Digit = 9 or 10 choices

For Units digit:{0-9} = 10 choices.

 

Here We can deduce Case 1 and Case 2 and add them.

Case 1: When Hundreds Digit = 0.

So we have,

9*1*9*10

Case 2: When Hundreds Digit = 1

So we have,

9*1*10*10

 

Adding both we get ,

9*1*9*10 + 9*1*10*10 = 9*10(9+10)=90*19 = 1710

[CTG1983]

I also get 1710.

 

Nuthan, Where were u in last few months?