deletions | additions       diff --git a/How_many_ways_can_we__.tex b/How_many_ways_can_we__.tex  index 6ad338c..632417e 100644  --- a/How_many_ways_can_we__.tex  +++ b/How_many_ways_can_we__.tex 
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For the first way, say we pick all blue candy. The stars represent candy and this is denoted...\\  $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$| \ | \\  For the second way, say we pick all red candy. Denoted...\\  \ |*******| |$\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$ $\bigstar$|  \ \\ For the third way, say we pick 2 blues, 2 reds and 3 green candies. Denoted...\\  **|**|*** $\bigstar$ $\bigstar$|$\bigstar$ $\bigstar$|$\bigstar$ $\bigstar$ $\bigstar$  \\ 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.