Question

When I drive to school every day, I pass eight traffic lights, each either green, yellow, or red. I find that, because of synchronization, a green light is always followed immediately by a yellow, and a red light is never immediately followed by a red. Thus a sequence of lights may start with GYRY, but not RRGG. How many possible sequences of the eight lights are there?

Answer 1

There are 48 possible sequences of the eight traffic lights satisfying the given conditions.

Explanation:

Since each green light is followed by a yellow light, there will be four pairs of GY in the sequence. We can represent these four pairs as follows: GY GY GY GY

we need to arrange the remaining four lights, which are red (R) lights. bc a red light is never followed by another red light, we got the following possibilities for the arrangement of the remaining four lights:

R R R R

RR R R

R RR R

R R RR

RR RR

RRR R

RR RR

R R R RR

R R RR R

• 4 arrangements with all four lights as R
• 1 arrangement with two RR and two R
• 2 arrangements with one RR and three R
• 2 arrangements with three R and one RR
• 2 arrangements with two RR and one R
• 1 arrangement with one R and two RR

Total possible sequences = Total GY pairs * Total arrangements of red lights

Total possible sequences = 4 * 12 = 48