iteration = 1: there are always t, 8 ways of selecting one object so each has probability 0.125 and the prob. of a score of 1 is 1 (!!) iteration = 2 results: $new = 1 1, freq = 56 $new = 2, freq = 8 Score frequencies: score n proportion ------ ------------ ------------ 1 56 0.875000000 2 8 0.125000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 2 8 0.125000000 1 64 1.000000000 O.K. total = 64 = expected total = 64 iteration = 3 results: $new = 1 1 1, freq = 336 $new = 2 1, freq = 168 $new = 3, freq = 8 Score frequencies: score n proportion ------ ------------ ------------ 1 336 0.656250000 2 168 0.328125000 3 8 0.015625000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 3 8 0.015625000 2 176 0.343750000 1 512 1.000000000 O.K. total = 512 = expected total = 512 iteration = 4 results: $new = 2 1 1, freq = 2016 $new = 1 1 1 1, freq = 1680 $new = 2 2, freq = 168 $new = 3 1, freq = 224 $new = 4, freq = 8 Score frequencies: score n proportion ------ ------------ ------------ 1 1680 0.410156250 2 2184 0.533203125 3 224 0.054687500 4 8 0.001953125 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 4 8 0.001953125 3 232 0.056640625 2 2416 0.589843750 1 4096 1.000000000 O.K. total = 4096 = expected total = 4096 iteration = 5 results: $new = 2 2 1, freq = 5040 $new = 3 1 1, freq = 3360 $new = 2 1 1 1, freq = 16800 $new = 1 1 1 1 1, freq = 6720 $new = 3 2, freq = 560 $new = 4 1, freq = 280 $new = 5, freq = 8 Score frequencies: score n proportion ------ ------------ ------------ 1 6720 0.205078125 2 21840 0.666503906 3 3920 0.119628906 4 280 0.008544922 5 8 0.000244141 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 5 8 0.000244141 4 288 0.008789062 3 4208 0.128417969 2 26048 0.794921875 1 32768 1.000000000 O.K. total = 32768 = expected total = 32768 iteration = 6 results: $new = 1 1 1 1 1 1, freq = 20160 $new = 2 2 2, freq = 5040 $new = 3 2 1, freq = 20160 $new = 4 1 1, freq = 5040 $new = 2 2 1 1, freq = 75600 $new = 3 1 1 1, freq = 33600 $new = 2 1 1 1 1, freq = 100800 $new = 3 3, freq = 560 $new = 4 2, freq = 840 $new = 5 1, freq = 336 $new = 6, freq = 8 Score frequencies: score n proportion ------ ------------ ------------ 1 20160 0.076904297 2 181440 0.692138672 3 54320 0.207214355 4 5880 0.022430420 5 336 0.001281738 6 8 0.000030518 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 6 8 0.000030518 5 344 0.001312256 4 6224 0.023742676 3 60544 0.230957031 2 241984 0.923095703 1 262144 1.000000000 O.K. total = 262144 = expected total = 262144 iteration = 7 results: $new = 2 1 1 1 1 1, freq = 423360 $new = 3 2 2, freq = 35280 $new = 2 2 2 1, freq = 176400 $new = 3 3 1, freq = 23520 $new = 4 2 1, freq = 35280 $new = 5 1 1, freq = 7056 $new = 3 2 1 1, freq = 352800 $new = 4 1 1 1, freq = 58800 $new = 2 2 1 1 1, freq = 705600 $new = 3 1 1 1 1, freq = 235200 $new = 4 3, freq = 1960 $new = 5 2, freq = 1176 $new = 6 1, freq = 392 $new = 7, freq = 8 $new = 1 1 1 1 1 1 1, freq = 40320 Score frequencies: score n proportion ------ ------------ ------------ 1 40320 0.019226074 2 1305360 0.622444153 3 646800 0.308418274 4 96040 0.045795441 5 8232 0.003925323 6 392 0.000186920 7 8 0.000003815 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 7 8 0.000003815 6 400 0.000190735 5 8632 0.004116058 4 104672 0.049911499 3 751472 0.358329773 2 2056832 0.980773926 1 2097152 1.000000000 O.K. total = 2097152 = expected total = 2097152 iteration = 8 results: $new = 4 4, freq = 1960 $new = 5 3, freq = 3136 $new = 6 2, freq = 1568 $new = 7 1, freq = 448 $new = 8, freq = 8 $new = 2 1 1 1 1 1 1, freq = 1128960 $new = 2 2 1 1 1 1, freq = 4233600 $new = 3 1 1 1 1 1, freq = 1128960 $new = 3 3 2, freq = 94080 $new = 4 2 2, freq = 70560 $new = 3 2 2 1, freq = 1411200 $new = 2 2 2 1 1, freq = 2822400 $new = 2 2 2 2, freq = 176400 $new = 1 1 1 1 1 1 1 1, freq = 40320 $new = 4 3 1, freq = 94080 $new = 5 2 1, freq = 56448 $new = 6 1 1, freq = 9408 $new = 3 3 1 1, freq = 470400 $new = 4 2 1 1, freq = 705600 $new = 5 1 1 1, freq = 94080 $new = 3 2 1 1 1, freq = 3763200 $new = 4 1 1 1 1, freq = 470400 Score frequencies: score n proportion ------ ------------ ------------ 1 40320 0.002403259 2 8361360 0.498375893 3 6867840 0.409355164 4 1342600 0.080025196 5 153664 0.009159088 6 10976 0.000654221 7 448 0.000026703 8 8 0.000000477 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 8 8 0.000000477 7 456 0.000027180 6 11432 0.000681400 5 165096 0.009840488 4 1507696 0.089865685 3 8375536 0.499220848 2 16736896 0.997596741 1 16777216 1.000000000 O.K. total = 16777216 = expected total = 16777216 iteration = 9 results: $new = 2 2 2 1 1 1, freq = 25401600 $new = 5 4, freq = 7056 $new = 6 3, freq = 4704 $new = 7 2, freq = 2016 $new = 8 1, freq = 504 $new = 9, freq = 8 $new = 2 2 1 1 1 1 1, freq = 15240960 $new = 3 1 1 1 1 1 1, freq = 3386880 $new = 3 3 3, freq = 94080 $new = 3 2 1 1 1 1, freq = 25401600 $new = 4 1 1 1 1 1, freq = 2540160 $new = 4 3 2, freq = 423360 $new = 5 2 2, freq = 127008 $new = 3 3 2 1, freq = 4233600 $new = 4 2 2 1, freq = 3175200 $new = 3 2 2 1 1, freq = 25401600 $new = 2 2 2 2 1, freq = 6350400 $new = 3 2 2 2, freq = 2116800 $new = 2 1 1 1 1 1 1 1, freq = 1451520 $new = 6 2 1, freq = 84672 $new = 4 3 1 1, freq = 2116800 $new = 5 2 1 1, freq = 1270080 $new = 6 1 1 1, freq = 141120 $new = 3 3 1 1 1, freq = 5644800 $new = 4 2 1 1 1, freq = 8467200 $new = 5 1 1 1 1, freq = 846720 $new = 4 4 1, freq = 105840 $new = 5 3 1, freq = 169344 $new = 7 1 1, freq = 12096 Score frequencies: score n proportion ------ ------------ ------------ 2 48444480 0.360939503 3 66279360 0.493819714 4 16828560 0.125382543 5 2420208 0.018031955 6 230496 0.001717329 7 14112 0.000105143 8 504 0.000003755 9 8 0.000000060 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 9 8 0.000000060 8 512 0.000003815 7 14624 0.000108957 6 245120 0.001826286 5 2665328 0.019858241 4 19493888 0.145240784 3 85773248 0.639060497 2 134217728 1.000000000 1 134217728 1.000000000 O.K. total = 134217728 = expected total = 134217728 iteration = 10 results: $new = 2 2 1 1 1 1 1 1, freq = 25401600 $new = 6 2 1 1, freq = 2116800 $new = 4 3 1 1 1, freq = 28224000 $new = 5 2 1 1 1, freq = 16934400 $new = 6 1 1 1 1, freq = 1411200 $new = 4 4 1 1, freq = 2646000 $new = 5 4 1, freq = 423360 $new = 5 3 1 1, freq = 4233600 $new = 7 1 1 1, freq = 201600 $new = 6 3 1, freq = 282240 $new = 7 2 1, freq = 120960 $new = 8 1 1, freq = 15120 $new = 2 2 2 1 1 1 1, freq = 127008000 $new = 3 1 1 1 1 1 1 1, freq = 4838400 $new = 3 2 2 1 1 1, freq = 254016000 $new = 2 2 2 2 1 1, freq = 95256000 $new = 5 5, freq = 7056 $new = 6 4, freq = 11760 $new = 7 3, freq = 6720 $new = 8 2, freq = 2520 $new = 9 1, freq = 560 $new = 3 2 1 1 1 1 1, freq = 101606400 $new = 4 1 1 1 1 1 1, freq = 8467200 $new = 4 3 3, freq = 705600 $new = 3 3 3 1, freq = 4704000 $new = 3 3 1 1 1 1, freq = 42336000 $new = 4 2 1 1 1 1, freq = 63504000 $new = 5 1 1 1 1 1, freq = 5080320 $new = 10, freq = 8 $new = 4 3 2 1, freq = 21168000 $new = 5 2 2 1, freq = 6350400 $new = 3 3 2 1 1, freq = 84672000 $new = 4 2 2 1 1, freq = 63504000 $new = 4 4 2, freq = 529200 $new = 5 3 2, freq = 846720 $new = 6 2 2, freq = 211680 $new = 3 2 2 2 1, freq = 84672000 $new = 2 2 2 2 2, freq = 6350400 $new = 3 3 2 2, freq = 10584000 $new = 4 2 2 2, freq = 5292000 Score frequencies: score n proportion ------ ------------ ------------ 10 8 0.000000007 2 254016000 0.236570835 3 587428800 0.547085702 4 194040000 0.180713832 5 33875856 0.031549349 6 4033680 0.003756657 7 329280 0.000306666 8 17640 0.000016429 9 560 0.000000522 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 10 8 0.000000007 9 568 0.000000529 8 18208 0.000016958 7 347488 0.000323623 6 4381168 0.004080281 5 38257024 0.035629630 4 232297024 0.216343462 3 819725824 0.763429165 2 1073741824 1.000000000 1 1073741824 1.000000000 O.K. total = 1073741824 = expected total = 1073741824 iteration = 11 results: $new = 3 2 1 1 1 1 1 1, freq = 186278400 $new = 6 2 1 1 1, freq = 31046400 $new = 4 4 1 1 1, freq = 38808000 $new = 5 5 1, freq = 465696 $new = 5 3 1 1 1, freq = 62092800 $new = 7 1 1 1 1, freq = 2217600 $new = 6 4 1, freq = 776160 $new = 7 3 1, freq = 443520 $new = 8 2 1, freq = 166320 $new = 9 1 1, freq = 18480 $new = 4 1 1 1 1 1 1 1, freq = 13305600 $new = 6 5, freq = 25872 $new = 7 4, freq = 18480 $new = 8 3, freq = 9240 $new = 9 2, freq = 3080 $new = 3 3 1 1 1 1 1, freq = 186278400 $new = 4 2 1 1 1 1 1, freq = 279417600 $new = 5 1 1 1 1 1 1, freq = 18627840 $new = 4 3 3 1, freq = 38808000 $new = 3 3 3 2, freq = 25872000 $new = 4 3 1 1 1 1, freq = 232848000 $new = 5 2 1 1 1 1, freq = 139708800 $new = 6 1 1 1 1 1, freq = 9313920 $new = 3 3 2 2 1, freq = 465696000 $new = 4 3 2 1 1, freq = 465696000 $new = 4 2 2 2 1, freq = 232848000 $new = 5 4 2, freq = 2328480 $new = 3 2 2 2 2, freq = 116424000 $new = 2 2 2 1 1 1 1 1, freq = 279417600 $new = 5 2 2 1 1, freq = 139708800 $new = 6 3 2, freq = 1552320 $new = 7 2 2, freq = 332640 $new = 10 1, freq = 616 $new = 2 2 2 2 1 1 1, freq = 698544000 $new = 8 1 1 1, freq = 277200 $new = 6 3 1 1, freq = 7761600 $new = 7 2 1 1, freq = 3326400 $new = 5 4 1 1, freq = 11642400 $new = 3 2 2 1 1 1 1, freq = 1397088000 $new = 2 2 2 2 2 1, freq = 209563200 $new = 3 2 2 2 1 1, freq = 1397088000 $new = 4 2 2 1 1 1, freq = 698544000 $new = 3 3 2 1 1 1, freq = 931392000 $new = 11, freq = 8 $new = 3 3 3 1 1, freq = 103488000 $new = 5 3 3, freq = 1552320 $new = 4 4 3, freq = 1940400 $new = 5 3 2 1, freq = 46569600 $new = 4 3 2 2, freq = 58212000 $new = 5 2 2 2, freq = 11642400 $new = 4 4 2 1, freq = 29106000 $new = 6 2 2 1, freq = 11642400 Score frequencies: score n proportion ------ ------------ ------------ 10 616 0.000000072 11 8 0.000000001 2 1187524800 0.138246082 3 4809604800 0.559911691 4 2089533600 0.243253727 5 434339136 0.050563730 6 62118672 0.007231565 7 6338640 0.000737915 8 452760 0.000052708 9 21560 0.000002510 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 11 8 0.000000001 10 624 0.000000073 9 22184 0.000002583 8 474944 0.000055291 7 6813584 0.000793206 6 68932256 0.008024771 5 503271392 0.058588501 4 2592804992 0.301842228 3 7402409792 0.861753918 2 8589934592 1.000000000 1 8589934592 1.000000000 O.K. total = 8589934592 = expected total = 8589934592