Three vehicles turn left and right

[robax25]

Homework Statement

consider an Experiment in which each of three vehicles taking a particular freeway exit turns left or right at the end of the exit ramp. The eight possible outcomes are posible. my question is that How to calculate 8 possible outcomes?

Relevant Equations

permutation p =nPr
combination C = nCr

I did combination like
3C2=3 here 3 means three vehicles. 2 means both turns left
3C2=3 here 3 means three vehicles. 2 means both turns right
3C3=1 3 means all are left.
3C3=1 3 means all are right.

My question is that is there another way that helps to get the answer?

 

[Office_Shredder]

You could just do there are 2 ways for the first vehicle to turn * 2 ways for the second vehicle to turn * 2 ways for the third vehicle to turn = 8 possibilities

 

[willem2]

I did combination like
3C2=3 here 3 means three vehicles. 2 means both turns left
3C2=3 here 3 means three vehicles. 2 means both turns right
3C3=1 3 means all are left.
3C3=1 3 means all are right.

My question is that is there another way that helps to get the answer?

You are really calculating (1+1)^3 by first expanding it as (1+1)(1+1)(1+1) = 1 + (3*1) + (3*1) + 1` = 8.
This will be valid for any number of cars, see Binomial Theorem Wikipedia