document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74653>Question 74653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a question from my son's homework.\r<BR>\n" );
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document.write( "\"If you have 4 horses and 4 stalls, how many different combinations can you stall the horses?\"\r<BR>\n" );
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document.write( "We have tried<BR>\n" );
document.write( "1 horse stalled 4 ways.  4 horses x 4 ways is 16.  But then I realize that more than one horse can be stalled togeather. So now I have confused myself so much I can't help my son. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53627 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a question from my son's homework.<BR>\n" );
document.write( "\"If you have 4 horses and 4 stalls, how many different combinations can you stall the horses?\"<BR>\n" );
document.write( "We have tried<BR>\n" );
document.write( "1 horse stalled 4 ways. 4 horses x 4 ways is 16. But then I realize that more than one horse can be stalled togeather. So now I have confused myself so much I can't help my son.<BR>\n" );
document.write( "YOUR ANSWER HOLDS FOR YOUR INITIAL BASIS OF 1 HORSE/1 HOUSE<BR>\n" );
document.write( "WELL YOUR DOUBT IS GENUINE.<BR>\n" );
document.write( "BUT THAT SHOULD BE A PART OF QUESTION.<BR>\n" );
document.write( "WHETHER 1 STALL CAN HOUSE ONLY 1 HORSE OR MORE.<BR>\n" );
document.write( "ASSUMING WE CAN PUT 0 TO 4 HORSES IN 1 , THE ANSWER IS AS FOLLOWS<BR>\n" );
document.write( "IF WE DENOTE X1,X2,X3,X4 ARE THE NUMBER OF HORSES IN THE 4 HOUSES,<BR>\n" );
document.write( "THEN THE PROBLEM IS EQUIVALENT TO FINDING NUMBER OF INTEGRAL <BR>\n" );
document.write( "SOLUTIONS FOR THE EQUATION <BR>\n" );
document.write( "X1+X2+X3++X4=4 WITH THE CONDITION THAT <BR>\n" );
document.write( "X1>=0,X2>=0,X3>=0 AND X4>=0<BR>\n" );
document.write( "THIS CAN BE TAKEN AS FINDING THE COEFFICIENT OF X^4 IN THE EXPANSION<BR>\n" );
document.write( "(X^0+X^1+X^2+X^3.......)^4 [HERE X^0 SIGNIFIES PUTTING 0 HORSES <BR>\n" );
document.write( "IN 1 HOUSE,X^1 MEANS PUTTING 1 HORSE IN 1 HOUSE ETC..POWER OF 4 FOR <BR>\n" );
document.write( "THE WHOLE SUM SIGNIFIES 4 HOUSES AS ALL THE 4 HOUSES HAVE SAME <BR>\n" );
document.write( "POSSIBILITY.<BR>\n" );
document.write( "THOUGH WE DONT NEED TO PUT BEYOND X^4,THERE IS NO HARM IN PUTTING<BR>\n" );
document.write( "THOSE TERMS,AS WE ARE FINALLY TAKING COEFFICIENT OF X^4 ONLY,<BR>\n" );
document.write( "AND THERE IS AN ADVANTAGE TO BE HAD AS YOU CAN SEE BELOW<BR>\n" );
document.write( "WE KNOW THAT <BR>\n" );
document.write( "1/(1-X)=1+X+X^2+X^3+.......<BR>\n" );
document.write( "SO WE HAVE TO FIND COEFFICIENT X^4 IN 1/(1-X)OR IN (1-X)^(-4)<BR>\n" );
document.write( "= USING BINOMIAL FORMULA....<BR>\n" );
document.write( "=[(-1)^4][(-4)(-5)(-6)(-7)/4!<BR>\n" );
document.write( "=840/24=35 </SPAN>\n" );
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