这道题用数学排列组合知识怎么做? 数学里排列组合知识的 C(5,3)就是用excel函数com...

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\uff08A)240 (B)180 (C)120 (D)60
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\u540c\u6837\u5f97\u51fa\u5171\u2474\u00d7\u2475\u00d7\u2476=240\u79cd\u3002
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\u7b2c\u4e8c\u7c7b\uff1a\u8fd9\u4e24\u4e2a\u4eba\u90fd\u53bb\u5f53\u8f66\u5de5\uff0cC\uff085,4\uff09\u00d7C\uff082,2\uff09\u00d7C\uff084,2\uff09=30\u79cd\uff1b
\u7b2c\u4e09\u7c7b\uff1a\u8fd9\u4e24\u4eba\u65e2\u4e0d\u53bb\u5f53\u94b3\u5de5\uff0c\u4e5f\u4e0d\u53bb\u5f53\u8f66\u5de5C\uff085,4\uff09\u00d7C\uff084,4\uff09=5\u79cd\u3002
\u7b2c\u56db\u7c7b\uff1a\u8fd9\u4e24\u4e2a\u4eba\u4e00\u4e2a\u53bb\u5f53\u94b3\u5de5\u3001\u4e00\u4e2a\u53bb\u5f53\u8f66\u5de5\uff0cC\uff082,1\uff09\u00d7C\uff085,3\uff09\u00d7C\uff084,3\uff09=80\u79cd\uff1b
\u7b2c\u4e94\u7c7b\uff1a\u8fd9\u4e24\u4e2a\u4eba\u4e00\u4e2a\u53bb\u5f53\u94b3\u5de5\u3001\u53e6\u4e00\u4e2a\u4e0d\u53bb\u5f53\u8f66\u5de5\uff0cC\uff082,1\uff09\u00d7C\uff085,3\uff09\u00d7C\uff084,4\uff09=20\u79cd\uff1b
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\u56e0\u800c\u5171\u6709185\u79cd\u3002
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\u65b9\u6cd5\u4e8c\uff1a
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\u56e0\u800c\u4e00\u5171\u670956-4+1=53\u4e2a\u3002
\u3010\u4f8b17\u3011 \u516d\u4eba\u6392\u6210\u4e00\u6392\uff0c\u8981\u6c42\u7532\u5728\u4e59\u7684\u524d\u9762\uff0c\uff08\u4e0d\u4e00\u5b9a\u76f8\u90bb\uff09\uff0c\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5? \u5982\u679c\u8981\u6c42\u7532\u4e59\u4e19\u6309\u4ece\u5de6\u5230\u53f3\u4f9d\u6b21\u6392\u5217\u5462?
\u5206\u6790\uff1a\uff08\u4e00\uff09\u5b9e\u9645\u4e0a\uff0c\u7532\u5728\u4e59\u7684\u524d\u9762\u548c\u7532\u5728\u4e59\u7684\u540e\u9762\u4e24\u79cd\u60c5\u51b5\u5bf9\u79f0\uff0c\u5177\u6709\u76f8\u540c\u7684\u6392\u6cd5\u6570\u3002\u56e0\u800c\u6709A(6\uff0c6)/2=360\u79cd\u3002
\uff08\u4e8c\uff09\u5148\u8003\u8651\u516d\u4eba\u5168\u6392\u5217A(6,6)\u79cd\uff1b\u5176\u6b21\u7532\u4e59\u4e19\u4e09\u4eba\u5b9e\u9645\u4e0a\u53ea\u80fd\u6309\u7167\u4e00\u79cd\u987a\u5e8f\u7ad9\u4f4d\uff0c\u56e0\u800c\u524d\u9762\u7684\u6392\u6cd5\u6570\u91cd\u590d\u4e86A(3,3)\u79cd\uff0c \u2234 \u6709A(6\uff0c6)/A(3,3)=120\u79cd\u3002
\u3010\u4f8b18\u30115\u75374\u5973\u6392\u6210\u4e00\u6392\uff0c\u8981\u6c42\u7537\u751f\u5fc5\u987b\u6309\u4ece\u9ad8\u5230\u77ee\u7684\u987a\u5e8f\uff0c\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5?
\u5206\u6790\uff1a\uff08\u4e00\uff09\u9996\u5148\u4e0d\u8003\u8651\u7537\u751f\u7684\u7ad9\u4f4d\u8981\u6c42\uff0c\u5171A\uff089,9\uff09\u79cd\uff1b\u7537\u751f\u4ece\u5de6\u81f3\u53f3\u6309\u4ece\u9ad8\u5230\u77ee\u7684\u987a\u5e8f\uff0c\u53ea\u6709\u4e00\u79cd\u7ad9\u6cd5\uff0c\u56e0\u800c\u4e0a\u8ff0\u7ad9\u6cd5\u91cd\u590d\u4e86A(5,5)\u6b21\u3002\u56e0\u800c\u6709A(9,9,)/A(5,5,)=9\u00d78\u00d77\u00d76=3024\u79cd
\u82e5\u7537\u751f\u4ece\u53f3\u81f3\u5de6\u6309\u4ece\u9ad8\u5230\u77ee\u7684\u987a\u5e8f\uff0c\u53ea\u6709\u4e00\u79cd\u7ad9\u6cd5\uff0c \u540c\u7406\u4e5f\u67093024\u79cd\uff0c\u7efc\u4e0a\uff0c\u67096048\u79cd\u3002
\uff08\u4e8c\uff09\u6309\u7167\u63d2\u7a7a\u7684\u65b9\u5f0f\u8fdb\u884c\u601d\u8003\u3002
\u7b2c\u4e00\u6b65\uff1a4\u4e2a\u5973\u751f\u5148\u57289\u4e2a\u4f4d\u7f6e\u4e2d\u9009\u62e94\u4e2a\uff0c\u4e3aA(9,4)\u79cd\u65b9\u5f0f\uff1b
\u7b2c\u4e8c\u6b65\uff1a\u7537\u751f\u7ad9\u5269\u4e0b\u7684\u4f4d\u7f6e\uff0c\u56e0\u4e3a\u5fc5\u987b\u4ece\u9ad8\u5230\u77ee\u7684\u987a\u5e8f\uff0c\u6ca1\u6709\u89c4\u5b9a\u65b9\u5411\uff0c\u6240\u4ee5\u67092\u79cd\uff1b
\u7efc\u4e0a\uff0c\u603b\u7684\u7ad9\u6cd5\u6570\u6709A(9,4)\u00d72=6048\u79cd\u3002
\u3010\u4f8b19\u3011 \u4e09\u4e2a\u76f8\u540c\u7684\u7ea2\u7403\u548c\u4e24\u4e2a\u4e0d\u540c\u7684\u767d\u7403\u6392\u6210\u4e00\u884c\uff0c\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5?
\u5206\u6790\uff1a\u5148\u8ba4\u4e3a\u4e09\u4e2a\u7ea2\u7403\u4e92\u4e0d\u76f8\u540c\uff0c\u5171A\uff085,5\uff09=120\u79cd\u65b9\u6cd5\u3002
\u800c\u7531\u4e8e\u4e09\u4e2a\u7ea2\u7403\u6240\u5360\u4f4d\u7f6e\u76f8\u540c\u7684\u60c5\u51b5\u4e0b\uff0c\u5171A\uff083,3\uff09=6\u53d8\u5316\uff0c\u56e0\u800c\u5171A\uff085,5\uff09/A\uff083,3\uff09=20\u79cd\u3002
\u516c\u5f0fP\u662f\u6307\u6392\u5217\uff0c\u4eceN\u4e2a\u5143\u7d20\u53d6R\u4e2a\u8fdb\u884c\u6392\u5217\uff08\u5373\u6392\u5e8f\uff09\u3002\uff08P\u662f\u65e7\u7528\u6cd5\uff0c\u6559\u6750\u4e0a\u591a\u7528A\uff0cArrangement)
\u516c\u5f0fC\u662f\u6307\u7ec4\u5408\uff0c\u4eceN\u4e2a\u5143\u7d20\u53d6R\u4e2a\uff0c\u4e0d\u8fdb\u884c\u6392\u5217\uff08\u5373\u4e0d\u6392\u5e8f\uff09\u3002
\u6321\u677f\u7684\u4f7f\u7528
\u3010\u4f8b20\u301110\u4e2a\u540d\u989d\u5206\u914d\u5230\u516b\u4e2a\u73ed\uff0c\u6bcf\u73ed\u81f3\u5c11\u4e00\u4e2a\u540d\u989d\uff0c\u95ee\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u5206\u914d\u65b9\u6cd5?
\u5206\u6790\uff1a\u628a10\u4e2a\u540d\u989d\u770b\u6210\u5341\u4e2a\u5143\u7d20\uff0c\u5728\u8fd9\u5341\u4e2a\u5143\u7d20\u4e4b\u95f4\u5f62\u6210\u7684\u4e5d\u4e2a\u7a7a\u4e2d\uff0c\u9009\u51fa\u4e03\u4e2a\u4f4d\u7f6e\u653e\u7f6e\u6863\u677f\uff0c\u5219\u6bcf\u4e00\u79cd\u653e\u7f6e\u65b9\u5f0f\u5c31\u76f8\u5f53\u4e8e\u4e00\u79cd\u5206\u914d\u65b9\u5f0f\u3002\u56e0\u800c\u517136\u79cd\u3002
\u533a\u522b\u4e0e\u8054\u7cfb
\u6240\u6709\u7684\u6392\u5217\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u5148\u53d6\u7ec4\u5408\uff0c\u518d\u505a\u5168\u6392\u5217\uff1b\u540c\u6837\uff0c\u7ec4\u5408\u5982\u8865\u5145\u4e00\u4e2a\u9636\u6bb5\uff08\u6392\u5e8f\uff09\u53ef\u8f6c\u5316\u4e3a\u6392\u5217\u95ee\u9898\u3002
\u3010\u4f8b21\u3011\u7528\u6570\u5b570\uff0c1\uff0c2\uff0c3\uff0c4\uff0c5\u7ec4\u6210\u6ca1\u6709\u91cd\u590d\u6570\u5b57\u7684\u56db\u4f4d\u6570\uff0c
\u2474\u53ef\u7ec4\u6210\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u56db\u4f4d\u6570?
\u2475\u53ef\u7ec4\u6210\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u56db\u4f4d\u5076\u6570
\u2476\u53ef\u7ec4\u6210\u591a\u5c11\u4e2a\u80fd\u88ab3\u6574\u9664\u7684\u56db\u4f4d\u6570?
\u5206\u6790\uff1a\u2474\u6709A\uff086,4\uff09-A\uff085,3\uff09=300\u4e2a\u3002
\u2475\u5206\u4e3a\u4e24\u7c7b\uff1a0\u5728\u672b\u4f4d\uff0c\u5219\u6709A\uff085,3\uff09=60\u79cd\uff1a0\u4e0d\u5728\u672b\u4f4d\uff0c\u5219\u6709C\uff082,1\uff09\u00d7A\uff085,3\uff09-C\uff082,1\uff09\u00d7A\uff084,2\uff09=96\u79cd\u3002
\u2234 \u517160+96=156\u79cd\u3002
\u2476\u5148\u628a\u56db\u4e2a\u76f8\u52a0\u80fd\u88ab3\u6574\u9664\u7684\u56db\u4e2a\u6570\u4ece\u5c0f\u5230\u5927\u5217\u4e3e\u51fa\u6765\uff0c\u5373\u5148\u9009
0\uff0c1\uff0c2\uff0c3
0\uff0c1\uff0c3\uff0c5
0\uff0c2\uff0c3\uff0c4
0\uff0c3\uff0c4\uff0c5
1\uff0c2\uff0c4\uff0c5
\u5b83\u4eec\u6392\u5217\u51fa\u6765\u7684\u6570\u4e00\u5b9a\u53ef\u4ee5\u88ab3\u6574\u9664\uff0c\u518d\u6392\u5217\uff0c\u6709\uff1a4\u00d7[A\uff084,4\uff09-A\uff083,3\uff09]+A\uff084,4\uff09=96\u79cd\u3002
\u5206\u7ec4\u95ee\u9898
\u3010\u4f8b22\u3011 5\u540d\u5b66\u751f\u5206\u914d\u52304\u4e2a\u4e0d\u540c\u7684\u79d1\u6280\u5c0f\u7ec4\u53c2\u52a0\u6d3b\u52a8\uff0c\u6bcf\u4e2a\u79d1\u6280\u5c0f\u7ec4\u81f3\u5c11\u6709\u4e00\u540d\u5b66\u751f\u53c2\u52a0\uff0c\u5219\u5206\u914d\u65b9\u6cd5\u5171\u6709\u591a\u5c11\u79cd\uff1f
\u5206\u6790\uff1a\uff08\u4e00\uff09\u5148\u628a5\u4e2a\u5b66\u751f\u5206\u6210\u4e8c\u4eba\uff0c\u4e00\u4eba\uff0c\u4e00\u4eba\uff0c\u4e00\u4eba\u5404\u4e00\u7ec4\u3002
\u5176\u4e2d\u6d89\u53ca\u5230\u5e73\u5747\u5206\u6210\u56db\u7ec4\uff0c\u6709C\uff085,3\uff09=10\u79cd\u5206\u7ec4\u65b9\u6cd5\u3002\u53ef\u4ee5\u770b\u62104\u4e2a\u677f\u4e09\u4e2a\u677f\u4e0d\u7a7a\u7684\u9694\u677f\u6cd5\u3002
\uff08\u4e8c\uff09\u518d\u8003\u8651\u5206\u914d\u5230\u56db\u4e2a\u4e0d\u540c\u7684\u79d1\u6280\u5c0f\u7ec4\uff0c\u6709A\uff084,4\uff09=24\u79cd\uff0c
\u7531\uff08\u4e00\uff09\uff08\u4e8c\uff09\u53ef\u77e5\uff0c\u517110\u00d724=240\u79cd\u3002
\u51e0\u4f55\u95ee\u9898

\u3010\u4f8b23\u3011\u67d0\u533a\u67097\u6761\u5357\u5317\u5411\u8857\u9053\uff0c5\u6761\u4e1c\u897f\u5411\u8857\u9053\uff08\u5982\u53f3\u56fe\uff09
\u2474\u56fe\u4e2d\u5171\u6709\u591a\u5c11\u4e2a\u77e9\u5f62\uff1f
\u2475\u4eceA\u70b9\u5230B\u70b9\u6700\u8fd1\u7684\u8d70\u6cd5\u6709\u591a\u5c11\u79cd\uff1f
\u5206\u6790\uff1a\u2474\u57287\u6761\u7ad6\u7ebf\u4e2d\u4efb\u90092\u6761\uff0c5\u6761\u6a2a\u7ebf\u4e2d\u4efb\u90092\u6761\uff0c\u8fd9\u68374\u6761\u7ebf
\u53ef\u7ec4\u62101\u4e2a\u77e9\u5f62\uff0c\u6545\u53ef\u7ec4\u6210\u77e9\u5f62C\uff087,2\uff09\u00b7C\uff085,2\uff09=210\u4e2a
\u2475\u6bcf\u6761\u4e1c\u897f\u5411\u7684\u8857\u9053\u88ab\u5206\u62104\u6bb5\uff0c\u6bcf\u6761\u5357\u5317\u5411\u7684\u8857\u9053\u88ab\u5206\u62106\u6bb5\uff0c\u4eceA\u5230B\u6700\u77ed\u7684\u8d70\u6cd5\uff0c\u65e0\u8bba\u600e\u6837\u8d70\uff0c\u4e00\u5b9a\u5305\u62ec10\u6bb5\uff0c\u5176\u4e2d6\u6bb5\u65b9\u5411\u76f8\u540c\uff0c\u53e6\u59164\u6bb5\u65b9\u5411\u76f8\u540c\uff0c\u6bcf\u79cd\u8d70\u6cd5\uff0c\u5373\u662f\u4ece10\u6bb5\u4e2d\u9009\u51fa6\u6bb5\uff0c\u8fd96\u6bb5\u662f\u8d70\u4e1c\u897f\u65b9\u5411\u7684\uff0c\u5171\u6709C\uff0810,6\uff09=C\uff0810,4\uff09=210\u79cd\u8d70\u6cd5\uff08\u540c\u6837\u53ef\u4ee5\u4ece10\u6bb5\u4e2d\u9009\u51fa4\u6bb5\u8d70\u5357\u5317\u65b9\u5411\uff0c\u6bcf\u4e00\u79cd\u9009\u6cd5\u5373\u662f1\u79cd\u8d70\u6cd5\uff09\u3002\u6240\u4ee5\u5171\u6709210\u79cd\u8d70\u6cd5\u3002

C(5,3)=(5\u00d74\u00d73)/(3\u00d72\u00d71)=10
\u4ecea\u3001b\u3001c\u3001d\u3001e\u8fd95\u4e2a\u5143\u7d20\u4e2d\u4efb\u53d63\u4e2a\u7684\u7ec4\u5408\u670910\u4e2a\uff1aabc\uff0cabd\uff0cabe\uff0cacd\uff0cace\uff0cade\uff0cbcd\uff0cbce\uff0cbde\uff0ccde\u3002

(1)6人住5房,必有1房有2人,选法有C(6,2),后全排列A(5,5)
故有1800种方法。
(2)5房空1房,有C(5,1)。
6人住4房:有3、1、1、1;此时有C(6,3),后全排列A(4,4)
有2、2、1、1;此时有C(6,2)C(4,2)/2,后全排列A(4,4)
共有1560种方法。
注:A(p,q)中p表示下标,q表示上标。

第一问,
先分组,其中有一组两个人,所以为C(6,2)
然后将5组作全排列,A55
所以答案=A55xC62=1800种
第二问
根据题意即将6个人分4组,需分类讨论。
其中一组3个人,其它三组1个人。即C63
其中两组2个人,其它两组1个人,即(C62xC42)/2
然后再将4组全排列A44
即可得
(C63+(C62xC42)/2)xA44=1560种
望采纳
谢谢
有任何不懂
请加好友
一一解答

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