Probability (1 Viewer)

[zeek]

Twelve people travel as passengers in three cars, each of which holds four passengers.
a) In how many ways can they make the journey, if it is immaterial in which car any party travels? Answer:5775
b) How many ways are there if two particular people must travel in different cars?
Answer: 4200

 

[Riviet]

a) no. of ways = (12C4.8C4.4C4)/3!

b) Assign the two guys first: 3 possible cars for first and and 2 possible for second guy
.'. 3 x 2 ways

Then assign remaining 10 people into the car with 4 spots, then the other two with 3 spots: 10C4.6C3.3C3

.'. total no. of ways = (3.2.10C4.6C3.3C3)/3!

* divide by 3! in each case because it doesn't matter which car the groups are in.