Ake sithi sineqoqo lezinto ezi-5, futhi sifuna ukukhetha ezi-3 zazo. Inani lezindlela zokwenza lokhu linikezwa inhlanganisela yefomula C(n, k) = n! / (k!(n - k)!), lapho u-n eyisamba senani lezinto, futhi u-k uyinani lezinto okufanele uzikhethe. Kulokhu, n = 5 futhi k = 3, ngakho C(5, 3) = 5! / (3!(5 - 3)!) = 5! / (3! * 2!) = (5 × 4 × 3 × 2 × 1) / ((3 × 2 × 1) × (2 × 1)) = (120) / (6 × 2) = 120 / 12 = 10. Ngakho-ke, kunezindlela eziyi-10 ezihlukene zokukhetha izinto ezi-3 eqoqweni lezinto ezi-5. Lesi sibalo sibonisa inani lezinhlanganisela ezingaba khona lapho kukhethwa isethi encane kusethi enkulu ngaphandle kokubheka ukuhleleka kokukhetha. Ifomula ehlanganisiwe iwusizo emikhakheni eyahlukene njengamathuba, izibalo, nama-combintorics wokubala inani lezindlela zokukhetha izinto eqenjini. Ukuqonda izinhlanganisela kusiza ekuxazululeni izinkinga ezihlobene nokukhetha nokuhlelwa kuzibalo nezimo zomhlaba wangempela. Sengiphetha, inani lezindlela zokukhetha izinto ezi-3 ku-5 yi-10, njengoba kubalwa kusetshenziswa ifomula yokuhlanganisa. Lesi sibonelo sibonisa ukusetshenziswa kwezibalo ezihlanganisiwe ekunqumeni ukukhetha okungaba khona. Izinhlanganisela ziwumqondo oyisisekelo kuzibalo ezihlukene futhi zinezinhlelo zokusebenza ezihlukene. Ifomula C(n, k) = n! / (k!(n - k)!) ibala kahle la manani ukuze anikezwe u-n no-k. Izibalo ezinjalo zibalulekile emikhakheni edinga ukubala kanye nokuhlola okungenzeka. Umphumela uqinisekisa ukuthi ezintweni ezi-5, kunamaqembu ayi-10 ahlukene ezinto ezi-3 lilinye. Le ndlela inganwetshwa kumasethi amakhulu kanye nosayizi abahlukene bokukhetha ngezinkinga ezihlukahlukene zokuhlanganisa.

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