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Austin Warby edited How_many_ways_can_we__.tex
over 8 years ago
Commit id: 478963e87d03539a6b77fc85ffed727bf69a10fc
deletions | additions
diff --git a/How_many_ways_can_we__.tex b/How_many_ways_can_we__.tex
index 632417e..d8542e5 100644
--- a/How_many_ways_can_we__.tex
+++ b/How_many_ways_can_we__.tex
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$\bigstar$ $\bigstar$|$\bigstar$ $\bigstar$|$\bigstar$ $\bigstar$ $\bigstar$ \\
Notice any scenario will result in 9 slots, 2 for the bars, and 7 for the stars(candies). \\
_ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\
Simply put all we are deciding in each case is where to put the bars. Therefore we have 9 slots choose 2 slots to place the bars or $\binom {9}{2}$. Equivelantly, we also have 9 slots choose 7 slots to place the stars or $\binom {9}{7}$. Feel free to verify that those are indeed the same.
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To finish the problem $\binom{9}{2}= \frac{9!}{7!2!}=36$ different ways to place the candies.