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<HEAD><TITLE>ChoosePeople</TITLE></HEAD>

<BODY BGCOLOR=beige STYLE="font-size:30px;font-family:Arial"><CENTER><H1 style="font-size:50px;font-family:Arial">Choose a Team of People</H1>

<BR><FORM NAME="myform" STYLE="font-size:50px">
There are <SELECT NAME=totalbox STYLE="font-size:50px">
<SCRIPT><!--
for (r=2; r<=20; r++)
	if (r==5) document.write("<OPTION SELECTED>5"); else document.write("<OPTION>"+r);
//--></SCRIPT></SELECT>
 people altogether.
<BR><BR>One of them is called A, and another is called B.
<BR><BR>Choose a team of <SELECT NAME=teambox STYLE="font-size:50px">
<SCRIPT><!--
for (r=1; r<=20; r++)
	if (r==3) document.write("<OPTION SELECTED>3"); else document.write("<OPTION>"+r);
//--></SCRIPT></SELECT>
 from these people.
<BR><BR><BR><INPUT TYPE=button NAME=submit VALUE="Choose" STYLE="font-size:50px" ONCLICK=choose()>

</FORM>

<SCRIPT><!--
function choose()
{
total = document.myform.totalbox.options[document.myform.totalbox.selectedIndex].text.valueOf();
team = document.myform.teambox.options[document.myform.teambox.selectedIndex].text.valueOf();
total = Math.round(total);
team = Math.round(team);

document.write("<BODY BGCOLOR=beige><CENTER><FONT SIZE=40><FONT FAMILY=Arial><FONT COLOR=red>");
if (team>total) document.write("Too few people to choose from.");
else	{
	document.write("A B <FONT COLOR=blue>");
	for (r=3; r<=total; r++)
		document.write("C<SUB>" + r + " </SUB> ");
	document.write("</CENTER><BR><FONT COLOR=black>");
	document.write("Number of ways of choosing <FONT COLOR=red>" + team + " ");
	if (team>1) document.write("people"); else document.write("person");
	document.write("<FONT COLOR=black> from " + total + " people = ");
	document.write("<SUP>" + total + "</SUP>C<SUB>" + team + "</SUB>");
	document.write(" = " + nCr(total, team));

	document.write("<BR><BR>Number of ways with <FONT COLOR=red>both A & B<FONT COLOR=black> in the team");
	if (total>=team) document.write(" = <SUP>" + (total-2) + "</SUP>C<SUB>" + (team-2) + "</SUB>");
	document.write(" = " + nCr(total-2, team-2));
 
	document.write("<BR><BR>Number of ways with <FONT COLOR=blue>neither A nor B<FONT COLOR=black> in the team");
	if (total-2>=team) document.write(" = <SUP>" + (total-2) + "</SUP>C<SUB>" + team + "</SUB>");
	document.write(" = " + nCr(total-2, team));
 
	document.write("<BR><BR>Number of ways with <FONT COLOR=green>at most 1 of A or B<FONT COLOR=black> in the team ");
	document.write(" = " + nCr(total, team) + " - " + nCr(total-2, team-2));
	document.write(" = " + (nCr(total, team) - nCr(total-2, team-2)));
 
	document.write("<BR><BR>Number of ways with <FONT COLOR=green>at least 1 of A or B<FONT COLOR=black> in the team ");
	document.write(" = " + nCr(total, team) + " - " + nCr(total-2, team));
	document.write(" = " + (nCr(total, team) - nCr(total-2, team)));
 
	} //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 (r>=0 && n>=r) return factorial(n)/factorial(n - r)/factorial(r);
	else return 0;
	} //end of function nCr

//--></SCRIPT>
</CENTER>

<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 3 children from 5 children
<BR>(i) if there are no restrictions
<BR>(ii) if 2 particular children must be included

<BR><BR>Find the number of teams of 11 that can be selected from 15 players
<BR>(i) if there are no restrictions
<BR>(ii) if the 2 youngest players are to be included

<BR><BR>Find the number of teams of 6 that can be selected from 10 players
<BR>(i) if both of the 2 oldest players are to be included
<BR>(ii) if at most 1 of the 2 oldest players are to be included




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