combinatorics problem - discrete math

[viktoria.1047]

How many times per day form the digits on the 6-digit display of digital clocks sequence such that: H1 ≤ H2 ≤ M1 < M2 ≤ S1 < S2, (H1H2 : M1M2 : S1S2).
Thank you for all help

 

[khansaheb]

How many times per day form the digits on the 6-digit display of digital clocks sequence such that: H1 ≤ H2 ≤ M1 < M2 ≤ S1 < S2, (H1H2 : M1M2 : S1S2).
Thank you for all help

Please define the variable names that you chose.
Please share your work/thoughts regarding this problem.

 

[Dr.Peterson]

I think it's fairly clear what the question means; I'm a little curious why, in H1 ≤ H2 ≤ M1 < M2 ≤ S1 < S2, two of the comparisons are exclusive while the others are not, but it's not necessary to know that. One question to be asked, though, is what happens when a digit is missing.

I might start by thinking about all the possibilities for the hours. Clearly 11 and 12 are allowed; are 1, 2, 3, 4, 5, 6, 7, 8, and 9?

Then, as has been said, we'd like to see what you have tried, so we can know what help you need.

 

[Steven G]

I think it's fairly clear what the question means; I'm a little curious why, in H1 ≤ H2 ≤ M1 < M2 ≤ S1 < S2, two of the comparisons are exclusive while the others are not, but it's not necessary to know that. One question to be asked, though, is what happens when a digit is missing.

I might start by thinking about all the possibilities for the hours. Clearly 11 and 12 are allowed; are 1, 2, 3, 4, 5, 6, 7, 8, and 9?

Then, as has been said, we'd like to see what you have tried, so we can know what help you need.

@Dr.Peterson, I would think that each position could only contain 0-9. I am not sure what you mean by 11 and 12. Yes you can have ...1,1... and ...1,2....

 

[Dr.Peterson]

@Dr.Peterson, I would think that each position could only contain 0-9. I am not sure what you mean by 11 and 12. Yes you can have ...1,1... and ...1,2....

I said "possibilities for the hours", for which there are two digits. Isn't it clear that the hour can be 11 or 12, because and 1≤1 and 1≤2? I didn't say the digits can be 11 or 12.