Below is a small collection of straws (imagine there are actually 50 there).
Three of the straws have been marked A B and C. Assume those are the straws that were chosen.
If A was the first straw picked, it could have been any one of the 50 straws.
If B was second that leaves us with 49 straws to pick from (because 1 straw was already chosen for A).
Finally, B can be any one of the remaining 48 straws.
This gives us 50*49*48=117,600
We must remember, though, that once we have picked A B and C there can be many other ways to pick them.
We might have picked them in the order of B A and C, for example.
What this means is that for every three groups of straws, they might have been picked in 3! ways.
That is, 3*2*1.
Our final answer is 117,600/6 = 19,600
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