bc

70000/10/172
40.6976744186

clock.c

#include <stdio.h>

int main(void)
{
	int count[10] = {}, digits[4] = {}, oldDigits[4] = {};

	for (int h=0; h<24; ++h) {
		for (int m=0; m<60; ++m) {
			digits[0] = h/10;
			digits[1] = h%10;
			digits[2] = m/10;
			digits[3] = m%10;

			for (int i=0; i<4; ++i) {
				if (digits[i] != oldDigits[i])
					++count[digits[i]];
				oldDigits[i] = digits[i];
			}
			printf("%2i:%2i | %i%i%i%i\n", h, m, digits[0], digits[1], digits[2], digits[3]);
		}
	}

	for (int i=0; i<10; ++i)
		printf("%i: %i\n", i, count[i]);
  
  return 0;
}

results

0: 168
1: 172
2: 172
3: 171
4: 170
5: 170
6: 146
7: 146
8: 146
9: 146