Solve Travel Problem: 10 Fans in 3 Taxis

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Here is a problem that I need to solve in preparation of my exams
(I know how to use combinations, permutations, binomial coeeficcients, normal distributions):

Ten fans are traveling to a rugby match in three taxis that will hold 2, 4 and 5 passengers respectively. In how many ways is it possible to transport the 10 people to the rugby match.
:confused:
 
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1st 2 in taxi1 4 in Taxi2 and 4 in taxi3
2nd 2 in Taxi1 5 in taxi3 and 3 in Taxi2
3rd 1 in taxi1 5in taxi3 and 4 in taxi2
so there are 3 possible ways...thats because you have only one spare seat in all three taxis so the spare seat can be in all three taxis
 

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