<PRE><B>Question 460098</B>
a jazz band has prepared 18 selections for a concert tour. At each stop they will perform 10. How many different programs are possible? 
Ans: 18C10 = 43,758 
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How many programs are possible if they always begin with the same song and end with the same song?
# of ways to pick the 1st song 18.
# of ways to pick the last song 1 (if end song is the same as the begin song).
# of ways to pick the middle 8 songs :: 16C8 
Ans: 18*1*17C8 = 43758
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You say the answer to part 2 is 12870
That is the answer if the number of ways to choose the 1st 
song is 1 and the number of ways to choose the last
song is 1.  Then the remaining songs can be selected in
16C8 = 12870 ways.
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Comment: The problem statement is very ambiguous.  It allows
for several interpretations of what the author means.  Not
a well-defined problem.  Boo!!
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Cheers,
Stan H.

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