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Six cars pull up to a red light, one at a time. At the light, there are three lanes, one left-turn lane, one straight-going lane, and one right-turn lane. How many ways can the cars stack up so that all three lanes are occupied?

Note that if the first car turns left and the second goes straight, this is considered different from the first car going straight and the second car turning left. In other words, the cars are distinguishable, but pull up to the intersection in a fixed order.

 Mar 3, 2021
 #1
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 Mar 3, 2021
edited by cryptoaops  Mar 3, 2021
 #2
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First of all, I know that is incorrect because of the fact that n choose n is indistiguisable items, but the cars are distinguishable

 

So the answer given there is incorrect

jxc516  Mar 3, 2021
 #3
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Nevermind, I solved it. Thank you!

 Mar 3, 2021

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