How many 5 digit combinations for numbers 1- 25?

There are 9 1-digit numbers and 16-2 digit numbers. So a 5 digit combination is obtained as:

• Five 1-digit numbers and no 2-digit numbers: 126 combinations
• Three 1-digit numbers and one 2-digit number: 1344 combinations
• One 1-digit numbers and two 2-digit numbers: 1080 combinations

That makes a total of 2550 combinations.

This scheme does not differentiate between {13, 24, 5} and {1, 2, 3, 4, 5}. Adjusting for that would complicate the calculation considerably and reduce the number of combinations.