Question

11£®Ëæ»ú½«1£¬2£¬¡­£¬2n£¨n¡ÊN^*£¬n¡Ý2£©Õâ2n¸öÁ¬ÐøÕýÕûÊý·Ö³ÉA£¬BÁ½×飬ÿ×én¸öÊý£¬A×é×îСÊýΪa₁£¬×î´óÊýΪa₂£»B×é×îСÊýΪb₁£¬×î´óÊýΪb₂£¬¼Ç¦Î=a₂-a₁£¬¦Ç=b₂-b₁£®
£¨1£©µ±n=3ʱ£¬Çó¦ÎµÄ·Ö²¼ÁкÍÊýѧÆÚÍû£»
£¨2£©ÁîC±íʾʼþ¡°¦ÎÓë¦ÇµÄȡֵǡºÃÏàµÈ¡±£¬Ê¼þC·¢ÉúµÄ¸ÅÂÊΪp£¨C£©£®
¢Ùµ±n=2ʱ£¬Çóp£¨C£©£»
¢Úµ±n¡ÊN^*£¬n£¾2ʱ£¬Çóp£¨C£©£®

Answer 1

·ÖÎö £¨1£©µ±n=3ʱ£¬¦ÎµÄÈ¡Öµ¿ÉÄÜΪ2£¬3£¬4£¬5£¬Çó³öËæ»ú±äÁ¿¦ÎµÄ·Ö²¼ÁУ¬´úÈëÊýѧÆÚÍû¹«Ê½¿ÉµÃÆäÊýѧÆÚÍûE¦Î£®
£¨2£©¸ù¾ÝC±íʾʼþ¡°¦ÎÓë¦ÇµÄȡֵǡºÃÏàµÈ¡±£¬ÀûÓ÷ÖÀà¼Ó·¨Ô­Àí£¬¿ÉµÃʼþC·¢ÉúµÄ¸ÅÂÊP£¨C£©µÄ±í´ïʽ£»

½â´ð ½â£º£¨1£©µ±n=3ʱ£¬¦ÎµÄÈ¡Öµ¿ÉÄÜΪ2£¬3£¬4£¬5
ÆäÖÐP£¨¦Î=2£©=$\frac{4}{{C}_{6}^{3}}$=$\frac{1}{5}$£¬
P£¨¦Î=3£©=$\frac{6}{{C}_{6}^{3}}$=$\frac{3}{10}$£¬
P£¨¦Î=4£©=$\frac{6}{{C}_{6}^{3}}$=$\frac{3}{10}$£¬
P£¨¦Î=5£©=$\frac{4}{{C}_{6}^{3}}$=$\frac{1}{5}$£¬
¹ÊËæ»ú±äÁ¿¦ÎµÄ·Ö²¼ÁÐΪ£º

¦Î	2	3	4	5
P	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{3}{10}$	$\frac{1}{5}$

¦ÎµÄÊýѧÆÚÍûE£¨¦Î£©=2¡Á$\frac{1}{5}$+3¡Á$\frac{3}{10}$+4¡Á$\frac{3}{10}$+5¡Á$\frac{1}{5}$=$\frac{7}{2}$£®
£¨2£©¢Ùµ±n=2ʱ£¬P£¨C£©=2¡Á$\frac{1+1}{{C}_{4}^{2}}$=$\frac{2}{3}$£®
¢Úµ±n£¾2ʱ£¬P£¨C£©=2¡Á$\frac{1+1{+C}_{2}^{1}+{C}_{4}^{2}{+C}_{6}^{3}+¡­{+C}_{2n-4}^{n-2}}{{C}_{2n}^{n}}$£®

µãÆÀ ±¾Ì⿼²éÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁкÍÊýѧÆÚÍû£¬ÌâÄ¿×öÆðÀ´²»ÄÑ£¬ÔËËãÁ¿Ò²²»´ó£¬ÊôÓÚÖеµÌ⣮