8명이 토너먼트 경기를 한다.
이 때, 8명의 선수들 중 순위를 매기는데, 그에 따라 각각 a1, a2, ... a8이라 하자.
순위에 따라 승패는 무조건 결정된다. 즉, a1은 모든 상대를 이기고, a8은 모든 상대에게 진다.
이 때, a4가 2등을 하게 될 확률은?
(단, 대진표를 짤 때 상대가 같다 하더라도 위치가 다르면 다른 것으로 간주한다. 즉, a1-a5가 붙는 것과 a5-a1이 붙는 것은 다른 경우이다-쉽게 말해서 모두 다르게 본다고 생각하시면 됩니다)
좋아요
0
글쎄요
0
어려워요
0
Severity: Warning
Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 201
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 202
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/adad6cc505e3b84ca5f93483e582abe5.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 212
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_get_contents(http://latex.codecogs.com/gif.latex?%5Cfrac%7B8%5Ctimes%204%5Ctimes%5Cbinom%7B4%7D%7B3%7D3%21%5Ctimes%203%21%20%7D%7B8%21%7D): Failed to open stream: No route to host
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_get_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/adad6cc505e3b84ca5f93483e582abe5.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/adad6cc505e3b84ca5f93483e582abe5.gif): Failed to open stream: Operation not permitted
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 201
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 202
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/da307eb86d86caecf945cba81a94034c.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 212
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_get_contents(http://latex.codecogs.com/gif.latex?%5Cfrac%7B4%7D%7B35%7D): Failed to open stream: No route to host
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_get_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/da307eb86d86caecf945cba81a94034c.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/da307eb86d86caecf945cba81a94034c.gif): Failed to open stream: Operation not permitted
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once