iteration = 1: there are always t, 28 ways of selecting one object so each has probability 0.035714285714285712 and the prob. of a score of 1 is 1 (!!) iteration = 2 results: $new = 1 1, freq = 756 $new = 2, freq = 28 Score frequencies: score n proportion ------ ------------ ------------ 1 756 0.964285714 2 28 0.035714286 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 2 28 0.035714286 1 784 1.000000000 O.K. total = 784 = expected total = 784 iteration = 3 results: $new = 1 1 1, freq = 19656 $new = 2 1, freq = 2268 $new = 3, freq = 28 Score frequencies: score n proportion ------ ------------ ------------ 1 19656 0.895408163 2 2268 0.103316327 3 28 0.001275510 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 3 28 0.001275510 2 2296 0.104591837 1 21952 1.000000000 O.K. total = 21952 = expected total = 21952 iteration = 4 results: $new = 2 1 1, freq = 117936 $new = 1 1 1 1, freq = 491400 $new = 2 2, freq = 2268 $new = 3 1, freq = 3024 $new = 4, freq = 28 Score frequencies: score n proportion ------ ------------ ------------ 1 491400 0.799471574 2 120204 0.195563047 3 3024 0.004919825 4 28 0.000045554 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 4 28 0.000045554 3 3052 0.004965379 2 123256 0.200528426 1 614656 1.000000000 O.K. total = 614656 = expected total = 614656 iteration = 5 results: $new = 2 2 1, freq = 294840 $new = 3 1 1, freq = 196560 $new = 2 1 1 1, freq = 4914000 $new = 1 1 1 1 1, freq = 11793600 $new = 3 2, freq = 7560 $new = 4 1, freq = 3780 $new = 5, freq = 28 Score frequencies: score n proportion ------ ------------ ------------ 1 11793600 0.685261349 2 5208840 0.302657096 3 204120 0.011860293 4 3780 0.000219635 5 28 0.000001627 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 5 28 0.000001627 4 3808 0.000221262 3 207928 0.012081555 2 5416768 0.314738651 1 17210368 1.000000000 O.K. total = 17210368 = expected total = 17210368 iteration = 6 results: $new = 1 1 1 1 1 1, freq = 271252800 $new = 2 2 2, freq = 294840 $new = 3 2 1, freq = 1179360 $new = 4 1 1, freq = 294840 $new = 2 2 1 1, freq = 22113000 $new = 3 1 1 1, freq = 9828000 $new = 2 1 1 1 1, freq = 176904000 $new = 3 3, freq = 7560 $new = 4 2, freq = 11340 $new = 5 1, freq = 4536 $new = 6, freq = 28 Score frequencies: score n proportion ------ ------------ ------------ 1 271252800 0.562893251 2 199311840 0.413604172 3 11014920 0.022857733 4 306180 0.000635373 5 4536 0.000009413 6 28 0.000000058 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 6 28 0.000000058 5 4564 0.000009471 4 310744 0.000644844 3 11325664 0.023502577 2 210637504 0.437106749 1 481890304 1.000000000 O.K. total = 481890304 = expected total = 481890304 iteration = 7 results: $new = 2 1 1 1 1 1, freq = 5696308800 $new = 3 2 2, freq = 2063880 $new = 2 2 2 1, freq = 51597000 $new = 3 3 1, freq = 1375920 $new = 4 2 1, freq = 2063880 $new = 5 1 1, freq = 412776 $new = 3 2 1 1, freq = 103194000 $new = 4 1 1 1, freq = 17199000 $new = 2 2 1 1 1, freq = 1238328000 $new = 3 1 1 1 1, freq = 412776000 $new = 4 3, freq = 26460 $new = 5 2, freq = 15876 $new = 6 1, freq = 5292 $new = 7, freq = 28 $new = 1 1 1 1 1 1 1, freq = 5967561600 Score frequencies: score n proportion ------ ------------ ------------ 1 5967561600 0.442273269 2 6986233800 0.517770015 3 519409800 0.038494964 4 19289340 0.001429589 5 428652 0.000031769 6 5292 0.000000392 7 28 0.000000002 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 7 28 0.000000002 6 5320 0.000000394 5 433972 0.000032163 4 19723312 0.001461752 3 539133112 0.039956716 2 7525366912 0.557726731 1 13492928512 1.000000000 O.K. total = 13492928512 = expected total = 13492928512 iteration = 8 results: $new = 4 4, freq = 26460 $new = 5 3, freq = 42336 $new = 6 2, freq = 21168 $new = 7 1, freq = 6048 $new = 8, freq = 28 $new = 2 1 1 1 1 1 1, freq = 167091724800 $new = 2 2 1 1 1 1, freq = 56963088000 $new = 3 1 1 1 1 1, freq = 15190156800 $new = 3 3 2, freq = 5503680 $new = 4 2 2, freq = 4127760 $new = 3 2 2 1, freq = 412776000 $new = 2 2 2 1 1, freq = 4953312000 $new = 2 2 2 2, freq = 51597000 $new = 1 1 1 1 1 1 1 1, freq = 125318793600 $new = 4 3 1, freq = 5503680 $new = 5 2 1, freq = 3302208 $new = 6 1 1, freq = 550368 $new = 3 3 1 1, freq = 137592000 $new = 4 2 1 1, freq = 206388000 $new = 5 1 1 1, freq = 27518400 $new = 3 2 1 1 1, freq = 6604416000 $new = 4 1 1 1 1, freq = 825552000 Score frequencies: score n proportion ------ ------------ ------------ 1 125318793600 0.331704952 2 229059721800 0.606295686 3 22350444480 0.059159148 4 1041597900 0.002756994 5 30862944 0.000081691 6 571536 0.000001513 7 6048 0.000000016 8 28 0.000000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 8 28 0.000000000 7 6076 0.000000016 6 577612 0.000001529 5 31440556 0.000083220 4 1073038456 0.002840214 3 23423482936 0.061999362 2 252483204736 0.668295048 1 377801998336 1.000000000 O.K. total = 377801998336 = expected total = 377801998336 iteration = 9 results: $new = 2 2 2 1 1 1, freq = 341778528000 $new = 5 4, freq = 95256 $new = 6 3, freq = 63504 $new = 7 2, freq = 27216 $new = 8 1, freq = 6804 $new = 9, freq = 28 $new = 2 2 1 1 1 1 1, freq = 2255738284800 $new = 3 1 1 1 1 1 1, freq = 501275174400 $new = 3 3 3, freq = 5503680 $new = 3 2 1 1 1 1, freq = 341778528000 $new = 4 1 1 1 1 1, freq = 34177852800 $new = 4 3 2, freq = 24766560 $new = 5 2 2, freq = 7429968 $new = 3 3 2 1, freq = 1238328000 $new = 4 2 2 1, freq = 928746000 $new = 3 2 2 1 1, freq = 44579808000 $new = 2 2 2 2 1, freq = 11144952000 $new = 3 2 2 2, freq = 619164000 $new = 2 1 1 1 1 1 1 1, freq = 4511476569600 $new = 1 1 1 1 1 1 1 1 1, freq = 2506375872000 $new = 6 2 1, freq = 4953312 $new = 4 3 1 1, freq = 619164000 $new = 5 2 1 1, freq = 371498400 $new = 6 1 1 1, freq = 41277600 $new = 3 3 1 1 1, freq = 9906624000 $new = 4 2 1 1 1, freq = 14859936000 $new = 5 1 1 1 1, freq = 1485993600 $new = 4 4 1, freq = 6191640 $new = 5 3 1, freq = 9906624 $new = 7 1 1, freq = 707616 Score frequencies: score n proportion ------ ------------ ------------ 1 250637587200 0.236932108 2 712013833440 0.673079168 3 899403130080 0.085022156 4 50616657000 0.004784881 5 1874923848 0.000177240 6 46294416 0.000004376 7 734832 0.000000069 8 6804 0.000000001 9 28 0.000000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 9 28 0.000000000 8 6832 0.000000001 7 741664 0.000000070 6 47036080 0.000004446 5 1921959928 0.000181686 4 52538616928 0.004966568 3 951941747008 0.089988723 2 807208008140 0.763067892 1 105784559534 1.000000000 O.K. total = 10578455953408 = expected total = 10578455953408 iteration = 10 results: $new = 2 2 1 1 1 1 1 1, freq = 78950839968000 $new = 1 1 1 1 1 1 1 1 1 1, freq = 47621141568000 $new = 2 1 1 1 1 1 1 1 1, freq = 112786914240000 $new = 6 2 1 1, freq = 619164000 $new = 4 3 1 1 1, freq = 49533120000 $new = 5 2 1 1 1, freq = 29719872000 $new = 6 1 1 1 1, freq = 2476656000 $new = 4 4 1 1, freq = 773955000 $new = 5 4 1, freq = 24766560 $new = 5 3 1 1, freq = 1238328000 $new = 7 1 1 1, freq = 58968000 $new = 6 3 1, freq = 16511040 $new = 7 2 1, freq = 7076160 $new = 8 1 1, freq = 884520 $new = 2 2 2 1 1 1 1, freq = 18797819040000 $new = 3 1 1 1 1 1 1 1, freq = 15038255232000 $new = 3 2 2 1 1 1, freq = 3417785280000 $new = 2 2 2 2 1 1, freq = 1281669480000 $new = 5 5, freq = 95256 $new = 6 4, freq = 158760 $new = 7 3, freq = 90720 $new = 8 2, freq = 34020 $new = 9 1, freq = 7560 $new = 3 2 1 1 1 1 1, freq = 15038255232000 $new = 4 1 1 1 1 1 1, freq = 1253187936000 $new = 4 3 3, freq = 41277600 $new = 3 3 3 1, freq = 1375920000 $new = 3 3 1 1 1 1, freq = 569630880000 $new = 4 2 1 1 1 1, freq = 854446320000 $new = 5 1 1 1 1 1, freq = 68355705600 $new = 10, freq = 28 $new = 4 3 2 1, freq = 6191640000 $new = 5 2 2 1, freq = 1857492000 $new = 3 3 2 1 1, freq = 148599360000 $new = 4 2 2 1 1, freq = 111449520000 $new = 4 4 2, freq = 30958200 $new = 5 3 2, freq = 49533120 $new = 6 2 2, freq = 12383280 $new = 3 2 2 2 1, freq = 148599360000 $new = 2 2 2 2 2, freq = 11144952000 $new = 3 3 2 2, freq = 3095820000 $new = 4 2 2 2, freq = 1547910000 Score frequencies: score n proportion ------ ------------ ------------ 1 476211415680 0.160775359 10 28 0.000000000 2 211828387680 0.715161040 3 343655970840 0.116022864 4 227720263680 0.007688141 5 101245792536 0.000341819 6 3124873080 0.000010550 7 66134880 0.000000223 8 918540 0.000000003 9 7560 0.000000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 10 28 0.000000000 9 7588 0.000000000 8 926128 0.000000003 7 67061008 0.000000226 6 3191934088 0.000010776 5 104437726624 0.000352596 4 238164036342 0.008040737 3 367472374474 0.124063601 2 248575625127 0.839224641 1 296196766695 1.000000000 O.K. total = 296196766695424 = expected total = 296196766695424 iteration = 11 results: $new = 3 2 1 1 1 1 1 1, freq = 578972826432000 $new = 2 1 1 1 1 1 1 1 1 1, freq = 2619162786240000 $new = 6 2 1 1 1, freq = 54486432000 $new = 4 4 1 1 1, freq = 68108040000 $new = 5 5 1, freq = 27243216 $new = 5 3 1 1 1, freq = 108972864000 $new = 7 1 1 1 1, freq = 3891888000 $new = 6 4 1, freq = 45405360 $new = 7 3 1, freq = 25945920 $new = 8 2 1, freq = 9729720 $new = 9 1 1, freq = 1081080 $new = 4 1 1 1 1 1 1 1, freq = 41355201888000 $new = 6 5, freq = 349272 $new = 7 4, freq = 249480 $new = 8 3, freq = 124740 $new = 9 2, freq = 41580 $new = 3 3 1 1 1 1 1, freq = 27570134592000 $new = 4 2 1 1 1 1 1, freq = 41355201888000 $new = 5 1 1 1 1 1 1, freq = 2757013459200 $new = 4 3 3 1, freq = 11351340000 $new = 3 3 3 2, freq = 7567560000 $new = 4 3 1 1 1 1, freq = 3132969840000 $new = 5 2 1 1 1 1, freq = 1879781904000 $new = 6 1 1 1 1 1, freq = 125318793600 $new = 3 3 2 2 1, freq = 817296480000 $new = 4 3 2 1 1, freq = 817296480000 $new = 4 2 2 2 1, freq = 408648240000 $new = 5 4 2, freq = 136216080 $new = 3 2 2 2 2, freq = 204324120000 $new = 2 2 2 1 1 1 1 1, freq = 868459239648000 $new = 5 2 2 1 1, freq = 245188944000 $new = 6 3 2, freq = 90810720 $new = 7 2 2, freq = 19459440 $new = 10 1, freq = 8316 $new = 3 1 1 1 1 1 1 1 1, freq = 413552018880000 $new = 2 2 2 2 1 1 1, freq = 103388004720000 $new = 8 1 1 1, freq = 81081000 $new = 6 3 1 1, freq = 2270268000 $new = 7 2 1 1, freq = 972972000 $new = 5 4 1 1, freq = 3405402000 $new = 2 2 1 1 1 1 1 1 1, freq = 2481312113280000 $new = 3 2 2 1 1 1 1, freq = 206776009440000 $new = 2 2 2 2 2 1, freq = 2819672856000 $new = 3 2 2 2 1 1, freq = 18797819040000 $new = 4 2 2 1 1 1, freq = 9398909520000 $new = 3 3 2 1 1 1, freq = 12531879360000 $new = 11, freq = 28 $new = 3 3 3 1 1, freq = 181621440000 $new = 5 3 3, freq = 90810720 $new = 4 4 3, freq = 113513400 $new = 5 3 2 1, freq = 13621608000 $new = 4 3 2 2, freq = 17027010000 $new = 5 2 2 2, freq = 3405402000 $new = 4 4 2 1, freq = 8513505000 $new = 6 2 2 1, freq = 3405402000 $new = 1 1 1 1 1 1 1 1 1 1 1, freq = 857180548224000 Score frequencies: score n proportion ------ ------------ ------------ 1 857180548224 0.103355588 10 8316 0.000000000 11 28 0.000000000 2 607514181674 0.732517620 3 125941149734 0.151855074 4 965733412644 0.011644448 5 501164385321 0.000604285 6 185617460952 0.000022381 7 4910514840 0.000000592 8 90935460 0.000000011 9 1122660 0.000000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 11 28 0.000000000 10 8344 0.000000000 9 1131004 0.000000000 8 92066464 0.000000011 7 5002581304 0.000000603 6 190620042256 0.000022984 5 520226389547 0.000627269 4 101775605159 0.012271717 3 136118710250 0.164126792 2 743632891924 0.896644412 1 829350946747 1.000000000 O.K. total = 8293509467471872 = expected total = 8293509467471872