How do you get probability of 4 digit number is greater than 3251 but less than 8825 using only 1 2 3 5 7 9?

Answer 1

The first thing to do is find how many possible combinations of those numbers match the criteria. All numbers that start with 7 match it. And there are 5x4x3=60 possible numbers that start with 7. All numbers that start with 5 also match it, and there are 5x4x3=60 numbers that start with 5. All numbers that start with 35, 37 or 39 match it. And there are 4x3x3=36 numbers that do this. And finally, all numbers that start with 325, 327 and 329 match it, and there are 3x3=9 numbers that do this. In total this is 60+60+36+9=165 possible 4 digit numbers that match the criteria. The number of possible four digit numbers in total is 6x5x4x3 = 360.

This means the probability of a 4 digit number using only 1,2,3,5,7 and 9 being greater than 3251 but less than 8825 is 165/360 which can be simplified to 11/24.