SOLUTION: A van has 3 bench seats holding 3 people per bench. 9 passengers are going to get in the van: a couple, 3 family members, and 4 random people. The 3 family members will only go if

Algebra ->  Permutations -> SOLUTION: A van has 3 bench seats holding 3 people per bench. 9 passengers are going to get in the van: a couple, 3 family members, and 4 random people. The 3 family members will only go if       Log On


   

Question 927204: A van has 3 bench seats holding 3 people per bench. 9 passengers are going to get in the van: a couple, 3 family members, and 4 random people. The 3 family members will only go if they sit together on one bench and the couple will only go if they sit side by side. How many ways are there to arrange these passengers?
My answer: 5,120
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
_____
A B C
_____
D E F
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G H I

The Familiy can sit in 3!=6  ways on one of the 3 benches.
That's 3*6 = 18 ways to seat the family.

Suppose, for instance, that they sit in seats A,B, and C

Next we seat the couple in 2! ways on D&E, E&F, G&H, or H&I 

So there are 2*4=8 ways to seat the couple.

Then there are 4! = 24 ways to seat the random people.

Answer: 18*8*24 = 3456

Edwin