SOLUTION: Ten people are going on a skin-diving trip in 3 cars that will hold 2, 4 and 5 passengers respectively. How many ways is it possible to transport 10 people to the skin lodge?

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Question 1021261: Ten people are going on a skin-diving trip in 3 cars that will hold 2, 4 and 5 passengers respectively. How many ways is it possible to transport 10 people to the skin lodge?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Since there is room for 2+4+5=11 passengers but only 10 are going,
There are three cases in which a different car carries 1 person
less than its full capacity. 

Case 1.  The 2-passenger car carries only 1 person, the other two cars
are full.

10 choose 1, 9 choose 4, 5 choose 5

(10C1)(9C4)(5C5)

Case 1.  The 4-passenger car carries only 3 people, the other two cars
are full.

10 choose 2, 8 choose 3, 5 choose 5

(10C2)(8C3)(5C5)

Case 3.  The 5-passenger car carries only 4 people, the other two cars
are full.

10 choose 2, 8 choose 4, 4 choose 4

(10C2)(8C4)(4C4)

Grand total:  (10C1)(9C4)(5C5) + (10C2)(8C3)(5C5) + (10C2)(8C4)(4C4) =

(10)(126)(1) + (45)(56)(1) + (45)(70)(1) = 1260 + 2520 + 3150 = 6930

Edwin