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Combination
Posted:
Oct 6, 2008 5:37 PM


I need help with this. I am not sure if part (a.) is correct and was wondering if anybody can check that? Also part (b) I need help with. thanks Brad.
Consider 15 identical toothpicks arranged parallel to each other in 15 distinct spots: 
a.) How many ways are there to choose 5 of these toothpicks? (Hint: one example of a valid choice of 5 toothpicks would be ?first, third, ninth, tenth, twelfth?.)
b.) How many ways are there to choose 5 of these toothpicks if no two toothpicks can be next to each other? (Hint: one example of a valid choice is ?first, third, fifth, seventh, ninth?.) 
MY WORK:
part a) nCr = n! / (r! * (nr)!) 15C5 = 15! / (5! * (15  5)!) = 15! / (5! * 10!) = 3003
part b) I need help with?



