Question

There are 6 cars lined up next to each other, including: 1 green car, 2 yellow cars and 3 red cars. Calculate the probability that 2 vehicles of the same color are not stacked side by side

Answer 1

Explanation:

Total number of ways to arrange the cars

= 6! / (2! * 3!) = 60.

We represent the cars as G, Y and R.

We first arrange the G and Y cars in a row. There are 2 possible cases to investigate.

Case 1: YGY arrangement

The yellow cars are already not stacked side by side.

We have _Y_G_Y_, where the 4 empty spaces are possible places for the red cars to settle. Number of ways = 4C3 = 4.

Case 2: YYG or GYY arrangement

In order for the yellow cars to not be stacked side by side, a red car must be between them.

We have _YRY_G_ or _G_YRY_, where the 3 empty spaces are possible places for the remaining 2 red cars to settle.

Number of ways = 2 * 3C2 = 6.

Hence the probability of such an event

happening is (4 + 6)/60 = 1/6.

The answer is 1/6.