There are 99 palindromic numbers between 10 and 1000: 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616, 626, 636, 646, 656, 666, 676, 686, 696, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 808, 818, 828, 838, 848, 858, 868, 878, 888, 898, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999.
Answer:
steps below
Step-by-step explanation:
Total = 12+17+14 = 43
Without replacement:
C(12,5) / C(43,5) = (12!/5!*7!) / (43!/5!*38!) = (12*11*10*9*8) / (43*42*41*40*39)
= 95040 / 115511760
= 0.00082
≈ 0.082%
with replacement: 12/43*12/43*12/43*12/43*12/43 = 12⁵ / 43⁵
