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Topic: Combination
Replies: 3   Last Post: Oct 6, 2008 10:28 PM

 Messages: [ Previous | Next ]
 Brad Grillakis Posts: 4 Registered: 10/2/08
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:

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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?.)
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MY WORK:

part a)
nCr = n! / (r! * (n-r)!)
15C5 = 15! / (5! * (15 - 5)!)
= 15! / (5! * 10!)
= 3003

part b) I need help with?

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