Hello Guest,
Of the three-digit integers greater than $500$, how many have two digits that are equal to each other and the remaining digit different from the other two
500, 511, 522, 533, 544, 566, 577, 588, 599 (10)
600, 611, 622, 633, 644, 655, 677, 688, 699 (10)
700, 711, 722, 733 ,744 ,755 ,766, 788, 799 (10)
800, 811, 822, 833, 844, 855, 866, 877, 899 (10)
900, 911, 922, 933, 944, 955, 966, 977, 988 (10)
505, 515, 525, 535, 545, 565, 575, 585, 595 (10)
606, 616, 626, 636, 646, 656, 676, 686, 696 (10)
707, 717, 727, 737, 747, 757, 767, 787, 797 (10)
808, 818, 828, 838, 848, 858, 868, 878, 898 (10)
909, 919, 929, 939, 949, 959, 969, 979, 989 (10)
550, 551, 552, 553, 554, 556, 557, 558, 559 (10)
660, 661, 662, 663, 664, 665, 667, 668, 669 (10)
770, 771, 772, 773, 774, 775, 776, 778, 779 (19)
880, 881, 882, 883, 884, 885, 886, 887, 889 (10)
This gives 140 numbers, if it were so desired.
Hope that was helpful. ^^
Straight