Suppose that vehicles taking a particular freeway exit can t

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.

a) All outcomes in the event A that all three vehicles go in the same direction are             [ Select ]                      

[\"{RLS, RSL, LRS, LSR, SRL, SLR}\",

\"{RRR, LLL, SSS}\",

\"{RRL, RRS, RLR, RSR, LRR, SRR}\"]         .

b) All outcomes in the event B that all three vehicles take different directions are             [ Select ]                       [\"{RRL, RRS, RLR, RSR, LRR, SRR}\",

\"{RRR, LLL, SSS}\",

\"{RLS, RSL, LRS, LSR, SRL, SLR}\"]         .

c) All outcomes in the event C that exactly two of the three vehicles turn right             [ Select ]                       [\"{RRL, RRS, RLR, RSR, LRR, SRR}\",

\"{RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS}\",

\"{RRR, LLL, SSS, RLS, RSL, LRS, LSR, SRL, SLR}\"]         .

d) All outcomes in the even D that exactly two vehicles go in the same direction             [ Select ]                       [\"{RLS, RSL, LRS, LSR, SRL, SLR}\",

\"{RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS}\",

\"{RRL, RRS, RLR, RSR, LRR, SRR}\"]         .

Solution

a.

RRR, LLL, SSS [OPTION 2]

*********

B.

{RLS, RSL, LRS, LSR, SRL, SLR} [THEY MUST TAKE DIFFERENT DIRECTIONS, OR DIFFERENT LETTERS]

C.

{RRL, RRS, RLR, RSR, LRR, SRR} [must have 2 R\'s]

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{RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS} [must have 2 letters that are the same]