document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181307>Question 1181307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Robert and frank were shooting baskets. They scored 3 points for a long shot, 2 points for a regular basket and 1 point for a free throw. \r<BR>\n" );
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document.write( "1) List all the possible ways Robert could have scored 12 points?\r<BR>\n" );
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document.write( "2) What is the possibility of scoring 12 points with a free throw?\r<BR>\n" );
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document.write( "3) What is the possibility of scoring 12 points without a free throw? </SPAN>\n" );
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document.write( "1) List all the possible ways Robert could have scored 12 points.<br><BR>\n" );
document.write( "There is no value added in making a list of all the possible ways.  I'll leave that to you.<br><BR>\n" );
document.write( "There IS added value in seeing a logical way to determine the number of different ways 12 points could be scored.  And making the complete list will be easy once that is done.<br><BR>\n" );
document.write( "Note the following method can be used to logically make a count of the number of ways of using any set of three numbers to get a particular total.<br><BR>\n" );
document.write( "(i) 4 3-point shots: 1 way<BR>\n" );
document.write( "The 4 3-point shots is the whole 12 points; the number of 2-point shots must be 0<br><BR>\n" );
document.write( "(ii) 3 3-point shots: 2 ways<BR>\n" );
document.write( "The 3 3-point shots are 9 of the 12 points; there are 3 points left.  The number of 2-point shots can be either 0 or 1<br><BR>\n" );
document.write( "(iii) 2 3-point shots: 4 ways<BR>\n" );
document.write( "The 2 3-point shots are 6 of the 12 points; there are 6 points left.  The number of 2-point shots can be any number 0 to 3<br><BR>\n" );
document.write( "(iii) 1 3-point shot: 5 ways<BR>\n" );
document.write( "The 1 3-point shot is 3 of the 12 points; there are 9 points left.  The number of 2-point shots can be any number 0 to 4<br><BR>\n" );
document.write( "(iii) 0 3-point shots: 7 ways<BR>\n" );
document.write( "The 3-point shots are 0 of the 12 points; there are 12 points left.  The number of 2-point shots can be any number 0 to 6<br><BR>\n" );
document.write( "The total number of ways of scoring 12 points with 3-, 2-, and 1-point shots is 1+2+4+5+7 = 19.<br><BR>\n" );
document.write( "You can easily make the complete list from the above discussion.<br><BR>\n" );
document.write( "2) What is the possibility of scoring 12 points with a free throw?<BR>\n" );
document.write( "3) What is the possibility of scoring 12 points without a free throw?<br><BR>\n" );
document.write( "These two questions have no mathematical meaning; \"possibility\" is not a number in math.<br><BR>\n" );
document.write( "Presumably the questions that are asked should have been the probabilities that, if 12 points were scored, they were scored either with or without a free throw (1-point shot).<br><BR>\n" );
document.write( "Those probabilities can easily be determined by examining the complete list of all 19 ways of scoring 12 points.<br><BR>\n" );
document.write( "I leave that to you also.<br><BR>\n" );
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