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<HEAD><TITLE>ChooseBoysGirls</TITLE></HEAD>
<BODY BGCOLOR=beige STYLE="font-size:25px;font-family:Arial"><CENTER><H1 style="font-size:25px;font-family:Arial">Choose a Team of Boys & Girls</H1>

<FORM NAME="myform" STYLE="font-size:25px">
Choose a team of <SELECT NAME=teambox STYLE="font-size:25px">
<SCRIPT><!--
for (r=1; r<=20; r++)
	if (r==4) document.write("<OPTION SELECTED>4"); else document.write("<OPTION>"+r);
//--></SCRIPT></SELECT>
 children from <SELECT NAME=boybox STYLE="font-size:25px">
<SCRIPT><!--
for (r=2; r<=10; r++)
	if (r==5) document.write("<OPTION SELECTED>5"); else document.write("<OPTION>"+r);
//--></SCRIPT></SELECT>
 boys and <SELECT NAME=girlbox STYLE="font-size:25px">
<SCRIPT><!--
for (r=2; r<=10; r++)
	if (r==6) document.write("<OPTION SELECTED>6"); else document.write("<OPTION>"+r);
//--></SCRIPT></SELECT>
 girls.
<BR><BR><BR><INPUT TYPE=button NAME=submit STYLE="font-size:25px" VALUE="Choose" ONCLICK=choose()>

</FORM>

<SCRIPT><!--
function choose()
{
team = document.myform.teambox.options[document.myform.teambox.selectedIndex].text.valueOf();
boy = document.myform.boybox.options[document.myform.boybox.selectedIndex].text.valueOf();
girl = document.myform.girlbox.options[document.myform.girlbox.selectedIndex].text.valueOf();
team = Math.round(team);
boy = Math.round(boy);
girl = Math.round(girl);

document.write("<BODY BGCOLOR=beige><CENTER><FONT Size=25px COLOR=blue>");
if (team > (boy+girl)) document.write("Too few to choose from.");
else	{
	for (r=1; r<=boy; r++)
		document.write(" B<SUB>" + r + "</SUB> ");
	document.write("<FONT COLOR=red> ");
	for (r=1; r<=girl; r++)
		document.write(" G<SUB>" + r + "</SUB> ");
	document.write("</CENTER><BR><FONT COLOR=black>");
	document.write("Number of ways of choosing <FONT COLOR=green>" + team + " children<FONT COLOR=black> from <FONT COLOR=blue>" + boy + " boys<FONT COLOR=black> & <FONT COLOR=red>" + girl + " girls<FONT COLOR=black> = ");
	document.write("<SUP>" + (boy+girl) + "</SUP>C<SUB>" + team + "</SUB>");
	document.write(" = " + nCr(boy+girl, team));

	document.write("<BR>Number of ways with <FONT COLOR=blue>no boys<FONT COLOR=black> = ");
	document.write("<SUP>" + girl + "</SUP>C<SUB>" + team + "</SUB>");
	document.write(" = " + nCr(girl, team));

	document.write("<BR>Number of ways with <FONT COLOR=red>no girls<FONT COLOR=black> = ");
	document.write("<SUP>" + boy + "</SUP>C<SUB>" + team + "</SUB>");
	document.write(" = " + nCr(boy, team));
 
	document.write("<BR>Number of ways with <FONT COLOR=blue>exactly 1 boy<FONT COLOR=black> = ");
	document.write("<SUP>" + boy + "</SUP>C<SUB>1</SUB> <SUP>" + girl + "</SUP>C<SUB>" + (team-1) + "</SUB>");
	document.write(" = (" + boy + ")(" + nCr(girl, team-1) + ")");
	document.write(" = " + (boy*nCr(girl, team-1)));

	document.write("<BR>Number of ways with <FONT COLOR=red>exactly 1 girl<FONT COLOR=black> = ");
	document.write("<SUP>" + boy + "</SUP>C<SUB>" + (team-1) + "</SUB> <SUP>" + girl + "</SUP>C<SUB>1</SUB>");
	document.write(" = (" + nCr(boy, team-1) + ")(" + girl + ")");
	document.write(" = " + (nCr(boy, team-1)*girl));

	document.write("<BR>Number of ways with <FONT COLOR=green>at least 1 boy & at least 1 girl<FONT COLOR=black>");
	document.write(" = " + nCr(boy+girl, team) + " - " + nCr(girl, team) + " - " + nCr(boy, team));
	document.write(" = " + (nCr(boy+girl, team)-nCr(girl, team)-nCr(boy, team)));

	document.write("<BR>Number of ways with <FONT COLOR=green>at least 2 boys & at least 2 girls<FONT COLOR=black>");
	document.write(" = " + nCr(boy+girl, team) + " - " + nCr(girl, team) + " - " + nCr(boy, team) + " - " + (boy*nCr(girl, team-1)) + " - " + (girl*nCr(boy, team-1)));
	document.write(" = " + (nCr(boy+girl, team)-nCr(girl, team)-nCr(boy, team)-(boy*nCr(girl, team-1))-(girl*nCr(boy, team-1))));


	} //end of else

document.write("<BR><BR><BR><FORM NAME=back><INPUT TYPE=button NAME=back VALUE=Back ONCLICK=history.back()></FORM>");

} //end of function choose

function factorial(n)
	{
	if (n > 0) return n*factorial(n - 1);
	else return 1;
	} //end of function factorial

function nCr(n, r)
	{
	if (n>=r) return factorial(n)/factorial(n - r)/factorial(r);
	else return 0;
	} //end of function nCr

//--></SCRIPT>
</CENTER>

<P STYLE="font-size:25px;font-family:Arial">
<BR><BR><B>Note: If this page cannot run online, please save it to your computer first.
<BR><BR>Exercises for students</B>
<BR>Solve the following problems on paper and check your working using the above application:

<BR><BR>Find the number of ways of selecting 4 children from 5 boys & 6 girls
<BR>(i) if there are no restrictions
<BR>(ii) if there must be exactly 1 boy
<BR>(iii) if there must be at least 1 boy & at least 1 girl

<BR><BR>A team of 5 pupils are to be chosen from a class of 6 boys and 6 girls.
<BR>Find the no. of such teams that contain at least 1 boy & at least 1 girl.
<BR>Find the no. of such teams that contain at least 2 boys & at least 2 girls.

<BR><BR>A set of 20 students is made up of 10 JC1 and 10 JC2 students.
<BR>Five students are to be selected from the set, & the order of selection is unimportant. Find
<BR>(i) the total number of possible selections,
<BR>(ii) the no. of selections in which there are at least 2 JC1 and at least 2 JC2 students.




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