document.write( "Question 435686: How many ways are there for a horse race with four horses to finish if ties are possible?(Note: Any number of the four horses may tie.) My answer is 75, But I still doubt it. Can anyone give me a reason? \n" ); document.write( "
Algebra.Com's Answer #301511 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
How many ways are there for a horse race with four horses to finish if ties are possible?(Note: Any number of the four horses may tie.) My answer is 75,
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\n" ); document.write( "Note: Think of a four letter word.
\n" ); document.write( "with no repetition
\n" ); document.write( "with 2 letters the same
\n" ); document.write( "with 2 sets of 2 letters the same
\n" ); document.write( "with 3 letters the same
\n" ); document.write( "with all letters the same
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\n" ); document.write( "If there are no ties the number of orders is 4! = 24
\n" ); document.write( "If 2 tie the number of orders is 4!/2! = 12
\n" ); document.write( "If 2 tie and the other 2 tie the number of orders is 4!/[2!*2!] = 6
\n" ); document.write( "If 3 tie the number of orders is 4!/3! = 4
\n" ); document.write( "If 4 tie the number of orders is 4!/4! = 1
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\n" ); document.write( "Total # of orders is 24+12+4+1 = 47
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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