The total number of minutes in 12 hours is 12*60=720, so there would be 720 permutations. Take the minutes 00 to 59. There are 60 permutations, but how many combinations? 01 is the same combination as 10; 02 and 20; 03 and 30, 04 and 40, 05 and 50. So this reduces the combinations from 60 to 55; 12 and 21, 13 and 31, 14 and 41, 15 and 51 reduces from 55 to 51; 23 and 32, 24 and 42, 25 and 52 takes us to 48, then 46, then 45. So for every hour we have 45 combinations of the minutes digits. In the hours we have 01 and 10 only, so from 00:00 to 11:59 we have 11 combinations in the hours. That gives us a total combination of 11*45=495. But there are hours/minutes to think about: 00:01 and 01:00; 00:02 and 02:00; 00:03 and 03:00; etc. up to 00:09 and 09:00. So 495 is reduced to 486.