document.write( "Question 1115051: that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms.
\n" ); document.write( "She has all the red ones. \n" ); document.write( "

Algebra.Com's Answer #729995 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "It is very simple problem. Much simpler than you, probably, thought at the beginning.
\n" ); document.write( "Your major task is to read the condition attentively to maximally simplify it.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The total number of balls in the bag was initially 4 + 3 + 2 + 1 = 10.\r\n" );
document.write( "\r\n" );
document.write( "How many ways are there to grab 8 balls from 10 ?  - There are   =  =  = 45 ways.\r\n" );
document.write( "\r\n" );
document.write( "    It is the full space of events.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In how many ways she may have 4 red balls among those 8 she grabbed? - In   =  =  = 15 ways.\r\n" );
document.write( "\r\n" );
document.write( "    (just having 4 red, she can complement them by 4 other balls, choosing them arbitrary among 6 remaining balls).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the probability under the question is   =  = 33.33%\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------
\n" ); document.write( "On Combinations, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );