ä»0å°9è¿å个æ°åä¸ä»»å3个æ°åç»æä¸ä¸ªæ²¡æéå¤çä¸ä½æ°
å
±å¯ç»æ 9*9*8 = 648 个ãï¼æ³¨ ç¾ä½æ°åä¸å¯ä»¥æ¯0ï¼
ç¶åæ 1-9 åæ3ç»
A: 1 4 7
B: 2 5 8
C: 3 6 9
é¦å
计ç®ç±è¿9个æ°ç»æçå¯ä»¥è¢«3 æ´é¤çæ° æå¤å°ä¸ªã
Aç»çä¸ä¸ªæ°åä»»ææåå¯ä»¥ç»æ被3 æ´é¤çæ°åã
å
±æ P(3,3) = 3*2*1 = 6
åç BåCç»ä¹å¯åææ6个æ°åè½è¢«3æ´é¤ã
以ä¸å
±è®¡ 18个æ°å å¯ä»¥è¢«3 æ´é¤ã
ä»AãBãCç»ä¸ä»»æé1个æ°åï¼ç±è¿3个æ°ååå¯ææ被3æ´é¤çæ°
å
±æ C(3,1)*C(3,1)*C(3,1)*P(3,3) = 3*3*3 * 3*2*1 = 162个
以ä¸å计 å
±æ 18+162=180个æ°åå¯è¢«3æ´é¤ã
ä¸é¢åèèå«æ0çä¸ä½æ°ã
å¨Cç»ä¸ä»»æéåº2个æ°åï¼åå¯ä¸0ææ è½è¢«3æ´é¤çä¸ä½æ°
å
±æ C(3,2)*[P(3,3)-P(2,2)]=3*(3*2*1 - 2*1)= 12 个
å®ä»¬åå«æ¯ 306 309 360 390 603 609 630 690 903 906 930 960
C(3,2)è¡¨ç¤ºä» 3 6 9 å
±3个æ°åä¸æ½å2个æ°åçæ¹æ³æ°
P(3,3)表示 0 ä¸ä¸é¢æ½åºç2个æ°å å
±3个æ°å è¿è¡æåçç§ç±»æ°
P(2,2)表示 å¨ä¸é¢çæåä¸ï¼0 被æå¨ç¾ä½æ
åµä¸çç§ç±»æ°ã
AãBç»ä¸ä»»æéä¸ä¸ªï¼åå¯ä»¥ä¸0ææè½è¢«3æ´é¤çä¸ä½æ°å
å
±æ C(3,1)*C(3,1)*[P(3,3)-P(2,2)] = 3*3 *(3*2*1-2*1)= 36个ã
以ä¸å计 180+12+36=228ãå³ 648个æ°åä¸æ228个æ°å¯ä»¥è¢«3æ´é¤ãä¸è½è¢«3æ´é¤çæ°åç个æ°æ¯ 648-228 = 420ã
å æ¤ææ±æ¦ç为ï¼420/648 = 35/54
åçè
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ææ¥è¯è®º>>ç¸å
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9*10*10= 900
100-999ä¹é´è½è¢«3æ´é¤çä¸ä½æ°ï¼
102+3k (k=0,1,2...299)
æ»ä¸ªæ°ï¼300
å»ææéå¤æ°åç个æ°ï¼
3*3*9-2*9+2*3= 69
å100-999ä¹é´è½è¢«3æ´é¤ç没æéå¤æ°åçä¸ä½æ°ä¸ªæ°ï¼
300-69= 231
äºæ¯ä»»å3个æ°åç»æ没æéå¤æ°åçä¸ä½æ°ä¸ä¸è½è¢«3æ´é¤ç
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900-231= 669
æ以é¢è®¾ææ±æ¦çï¼
669/900= 223/300
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