My not-so-short computer code agrees with Melody's number:
a=0;b=0;c=0;d=0;e=0;f=0;g=0;p=0; cycle:n=a*1000000+b*100000+c*10000+d*1000+e*100+f*10+g; if(a*b*c*d*e*f*g==10000, goto loop, goto next);loop:printn,", ",;p=p+1; next:g++;if(g<10, goto cycle, 0);g=1;f++;if(f<10, goto cycle, 0);g=1;f=1;e++;if(e<10, goto cycle,0);g=1;f=1;e=1;d++;if(d<10, goto cycle,0);g=1;f=1;e=1;d=1;c++;if(c<10, goto cycle,0);g=1;f=1;e=1;d=1;c=1;b++;if(b<10, goto cycle,0);g=1;f=1;e=1;d=1;c=1;b=1;a++;if(a<10, goto cycle,0);print"Total = ",p
OUTPUT:
1255558 , 1255585 , 1255855 , 1258555 , 1285555 , 1445555 , 1454555 , 1455455 , 1455545 , 1455554 , 1525558,............................. 8525551 , 8551255 , 8551525 , 8551552 , 8552155 , 8552515 , 8552551 , 8555125 , 8555152 , 8555215 , 8555251 , 8555512 , 8555521 , Total = 420