问一个简单的排列组合问题
\u95ee\u4e00\u4e2a\u6392\u5217\u7ec4\u5408\u7684\u7b80\u5355\u95ee\u9898\u7528Ca/b\u8868\u793aCb\u53d6a,\u6bd4\u5982C2/3=C1/3=3
\u5206\u4ee5\u4e0b\u51e0\u79cd\u60c5\u51b5
1-1-1-7:C1/10*C1/9*C1/8*C7/7=720
1-1-2-6:C1/10*C1/9*C2/8*C6/6=?
1-1-3-5:C1/10*C1/9*C3/8*C5/5=?
1-1-4-4:C1/10*C1/9*C4/8*C4/4=?
1-2-2-5:C1/10*C2/9*C2/7*C5/5=?
1-2-3-4:C1/10*C2/9*C3/7*C4/4=?
1-3-3-3:C1/10*C3/9*C3/6*C3/3=?
\u4f60\u81ea\u5df1\u53bb\u8ba1\u7b97\u6bcf\u4e00\u79cd\u60c5\u51b5,\u7136\u540e\u5168\u90e8\u52a0\u8d77\u6765\u5c31\u53ef\u4ee5\u4e86.
[\u8bf4\u660e:\u7531\u4e8e\u53ea\u8bf4\u5206\u62104\u4e2a\u7ec4,\u6ca1\u8bf4\u6bcf\u4e2a\u7ec4\u591a\u5c11\u4eba,\u6240\u4ee5\u624d\u5206\u6210\u51e0\u79cd\u60c5\u51b5\u6765\u5206\u6790,\u6bd4\u59821-2-2-5,\u610f\u601d\u662f4\u4e2a\u7ec4\u7684\u4eba\u6570\u5206\u522b\u4e3a1,2,2,5.]
\u6211\u521a\u624d\u60f3\u6e05\u695a\u4e86,\u7684\u786e\u6709\u91cd\u590d!\u66f4\u6b63\u5982\u4e0b~
1-1-1-7:C3/10*C7/7 (3\u4e2a\u4eba\u81ea\u52a8\u5206\u62103\u7ec4)
1-1-2-6:C2/10*C2/8*C6/6
1-1-3-5:C2/10*C3/8*C5/5=?
1-1-4-4:C2/10*C4/8*C4/4=?
1-2-2-5:C1/10*C2/9*C2/7*C5/5=?
1-2-3-4:C1/10*C2/9*C3/7*C4/4=?
1-3-3-3:C1/10*C3/9*C3/6*C3/3=?
\u672c\u9898\u4e0d\u4ec5\u5171\u548c\u515a\u548c\u6c11\u4e3b\u515a\u4e4b\u95f4\u6709\u533a\u522b\uff0c\u5c31\u8fde\u5171\u548c\u515a\u5185\u90e8\u4e4b\u95f4\u6216\u6c11\u4e3b\u515a\u5185\u90e8\u4e4b\u95f4\u90fd\u5b58\u5728\u7740\u4e2a\u4f53\u5dee\u5f02\u7684\u533a\u522b\uff0c\u6240\u4ee5\u8fd9\u4e2a\u9898\u5e94\u8be5\u8981\u5168\u6392\u5217\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u5373P(9,9)=9!\uff0c\u672c\u9898\u5bb9\u6613\u505a\u9519\u7684\u5730\u65b9\u662f\uff0c\u4e00\u822c\u7b54\u9898\u8005\u53ea\u6ce8\u610f\u5230\u5171\u548c\u515a\u548c\u6c11\u4e3b\u515a\u7684\u533a\u522b\uff0c\u5ffd\u89c6\u4e863\u4e2a\u5171\u548c\u515a\u4e4b\u95f4\u7684\u533a\u548c6\u4e2a\u6c11\u4e3b\u515a\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u8fd9\u91cc\u5e94\u8be5\u5c31\u662f\u51fa\u9898\u8005\u7684\u7528\u610f\u6240\u5728\u4e86\uff01\uff01
26*26＝676种组合10*10*10＝1000种组合
26*26*10*10*10＝676000种组合
绛旓細姣忕彮鑷冲皯涓浜猴紝閭ｄ箞鎴戜滑鍏堜粠姣忕彮鍑涓涓浜猴紝闂灏卞彉鎴愪簡浣欎笅鐨5浜轰粠7涓彮涓娊鍙栥備細鍑虹幇浠ヤ笅鍑犵鎯呭喌锛1锛氫粠7涓彮涓换鎰忛変竴涓彮鐩存帴鎶藉嚭5鍚 鍏辨湁C锛7锛1锛夛紳7绉缁勫悎锛2锛氫粠7涓彮涓换鎰忛変簩涓彮锛岀敱杩欎袱涓彮鍑5鍚嶅鐢燂紝鍒欐娊鍙栫彮绾х殑鎯呭喌鏄細C锛7锛2锛夛紳21绉嶏紝鑰岃繖姣忎竴绉嶇彮绾х粍鍚堝張...
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绛旓細鍥犱负瑕侀夊嚭涓嶅悓骞寸骇鐨勪袱浜哄弬鍔犲競閲岀粍缁囩殑娲诲姩 鎵浠ユ瘡涓勾绾ф渶澶氬彧鑳介夊嚭1浜 濡傛灉涓や汉鏉ヨ嚜1銆2骞寸骇 鍒欐湁5*6=30绉嶉夋硶 鍚岀悊锛屽鏋滀袱浜烘潵鑷2銆3骞寸骇 鍒欐湁6*4=24绉嶉夋硶 濡傛灉涓や汉鏉ヨ嚜1銆3骞寸骇 鍒欐湁5*4=20绉嶉夋硶 鎵浠ワ紝鍏辨湁30+24+20=74绉嶄笉鍚岀殑閫夋硶 ...
绛旓細绗竴绉嶆濈淮鏂瑰紡锛2涓猯褰㈡垚3涓┖锛2涓猼鎻掔┖鏈3x3=9绉嶏紝鍐嶆妸鍓╀綑鐨勪袱涓彃鍏ヤ簲涓┖涓紙2涓猯,2涓猼浜х敓5涓┖锛夋墍浠ュ叡鏈9P(5,2)=180绉 绗簩绉嶏細鎺掑湪涓鎺掑叚涓┖浣嶏紝閫変袱涓粰l鏈塁(6,2),鍦ㄩ変袱涓粰t锛屾湁C(4,2),鍓╀綑涓や釜鍏鎺掑垪 鎵浠ユ湁C锛6锛2锛塁(4,2)P(2,2)=180涓 绗笁绉嶏細...
绛旓細鏃㈢劧B涓嚦灏戞湁7涓暟閲嶅悎,鍒欐儏鍐靛彲鑳芥槸鏈7,8,9鎴10涓暟閲嶅悎杩欏洓绉嶆儏鍐.鎴戜滑鍏堟潵鐪嬬涓绉嶆儏鍐,7涓暟閲嶅悎 鍏堥夊嚭鏄偅涓冧釜鏁伴噸鍚,鍒楀紡涓 7 C = 10*9*8/3/2 = 120 10 鎰忎负7涓暟閲嶅悎鏈120绉嶆儏鍐 閭ｄ箞杩樻湁鍙﹀涓変釜鏁板憿?鍐嶆潵鎺掑畠浠.杩欓噷瑕佹敞鎰,杩欎笁涓暟姣涓涓閮藉繀椤昏劚绂诲師鏉ョ殑浣嶇疆,姣斿...
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绛旓細灏戜簡闆嗗悎{b,c,e}.瀛愰泦涓暟C(5锛3)鍒嗗埆涓:abc,abd,abeacd,acebcd,bceade,cde,bde.鍏10涓皯鎺夌殑鏄瘂b,c,e}
绛旓細缁11涓汉 缂栧彿1锛2锛3锛4锛5锛6锛7锛8锛9锛10锛11 11涓汉瀹夋帓鍛ㄤ竴鍒板懆浜斿叡5澶╃殑鍊肩彮浠诲姟锛岃姹傛瘡浜烘伆濂藉间袱娆★紝姣忓ぉ鑷冲皯鏈4浜哄肩彮 鎵浠ユ垜鐜板湪灏卞彲浠ュ仛鍑涓涓璇捐〃绗﹀悎棰樼洰鎰忔濆涓嬶細鍛ㄤ竴 锛1 2 3 4 鍊肩彮 鍛ㄤ簩 锛1 2 3 4 鍊肩彮 鍛ㄤ笁 锛5 6 7 8 9 鍊肩彮 鍛ㄥ洓 锛...
绛旓細浠3鍚嶇敺鐢熷拰4鍚嶅コ鐢熶腑閫夊嚭5浜烘帓鎴愪竴鎺 濡傛灉閫夊嚭2鍚嶇敺鐢熷拰3鍚嶅コ鐢燂紝鍏辨湁=锛3鐢烽2鐢凤級X锛4濂抽3濂筹級X锛5浜哄叏鎺掑垪锛=C(2 3)C(3 4)A(5 5)=3x2x5!=1440 濡傛灉閫夊嚭2鍚嶇敺鐢熷拰3鍚嶅コ鐢燂紝鍏朵腑3鍚嶅コ鐢熷繀椤荤浉閭伙紝鍏辨湁=锛3鐢烽2鐢凤級X锛4濂抽3濂筹級X锛3濂冲叏鎺掑垪锛塜锛2鐢峰拰濂虫讳綋鍏ㄦ帓鍒...
