Can you check to see if I got all these sets right?

[mr_coffee]

Homework Statement

Supppose that vechiles taking a particular free way exit can turn right (r), left (l), or go straight (s). Consider observing the direction for each of three sucessive vechiles.

The Attempt at a Solution

So there is a total of 3^3 = 27 possiblities right.

a. list all outcomes in the event A that all three vechiles go in the same direction:
A = {rrr,lll,sss}

b. List all outcomes in the event B that all three vechiles take different directions:
B = {rls,rsl,srl,slr,lsr,lrs}

c. List all outcomes in event C that exactly tow of the three vchiles turn right.

C = {rrs,rrl,rsr,rlr,srr,lrr}

d. List all outcomes in the event D that exactly two vechiles turn the same directoin:
D = {rrs,rrl,rsr,rlr,srr,lrr,
lls, llr, lsl, lrl, sll, rll, ssl, ssr, sls, srs, lss, rss };

e. List all D';
D' = {rrr,lll,sss,rls, rsl, srl, slr, lsr, lrs, rrs, rrl, rsr, rlr, srr, lrr}
C U D = { rrs, rrl, rsr, rlr, srr, lrr, lls, llr, lsl, lrl , sll, rll, ssl, ssr, sls, srs, lss, rss};
C intersect D = { rrs, rrl, rsr, rlr, srr, lrr};To be a set, you can't have duplications right? so C U D, because C is a subset of D, that means I wouldn't rewrite the elements if D already has them correct? Like in C U D, I only wrote D.
Thanks.

 

[EnumaElish]

See http://en.wikipedia.org/wiki/Multinomial_distribution

Look at the paragraph that starts with "The support of the multinomial distribution..."