2 - тұжырым. .
Шынында да, әрбір Хi ішкі жиынын қайталанбайтын теру деп қарауға болады, олай болса,
Мысал. 25 адамнан тұратын топқа староста сайланды. 12 адам келісті, 10 қарсы болды, 3-і қалыс қалды. Мұндай сайлау қанша әдіспен жүргізіледі?
Енді i=1, 2, …, n үшін әрқайсысында i элементі бар mi ішкі жиыны бар болатын |X|=n, Х жиынын қанша ішкі жиынға бөлуге болатынын есептейік: Мұнда алдыңғы жағдайға қарағанда ішкі жиындарды таңдау реттелмеген. Мысалы, Х = {1, 2, 3, 4, 5}жиыны үшін келесі үш бөліктеу бірдей.
{1, 3}, {4}, {2, 5}; {4}, {2, 5}, {1, 3}; {2, 5}, {4}, {1, 3}
Бұл бөліктеуде m1=1, m2=2, m3=m4=m5=0.Аталған бөліктеулердің санын N(m1, m2, …, mn) арқылы белгілейміз. 3 - тұжырым.
Қарастырылып отырған реттелмеген бөліктеудің әрқайсысын m1!m2!…mn! тәсілмен төмендегі реттелген бөліктеуге түрлендіруге болады:
мұндағы,
![](data:image/png;base64,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. Мұндай реттелген бөліктеудің саны:
Ал реттелмеген бөліктеудің саны бұдан m1!…mn! есе аз.
Мысал. 25 адамнан тұратын топты әрқайсысы 5 адамнан 5 коалацияға қанша әдіспен топтастыруға болады? |X| = 25, m1=…=m4=0, m5=5, m6=…=m25=0;
N(0, 0, 0, 0, 5, 0, …, 0) = =5194672859376.
Достарыңызбен бөлісу: |