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At a local carnival, Mia is shooting at a row of 10 duck targets. Each time she shoots at a duck, the duck she shoots and any ducks immediately next to it fall down. In how many different ways can Mia shoot three ducks? (The order of the ducks also matters.)

 Mar 5, 2020
 #1
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Well  she  can  only shoot  at  ducks 2 through  9 because  there  is no duck to the left  of  duck 1  or to the right of duck 10

 

So.......the number  of  ways  (orders)  of ducks she  can shoot  is

 

[ 9 - 2  + 1 ] !   =   8!   =   40320   ways

 

 

cool cool cool

 Mar 5, 2020
 #2
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I think she can shoot the ducks 1 and 10, just only 2 ducks fall down, not three.

Guest Mar 5, 2020
 #3
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Also, just because a duck "falls down" doesn't mean that it was shot. Mia needs to fire at three ducks, knocking down at most 9 ducks and at least 6.

Guest Mar 5, 2020

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