A box contains 6 red balls, 4 white balls, and 5 green balls. If three balls are drawn in succession without being replaced, what is the probability that they are drawn in the order red, white, green?

3/12 or 1/4

To calculate the probability of drawing the balls in a specific order, we need to determine the total number of possible sequences of drawing three balls from the box and the number of sequences where the balls are drawn in the order red, white, green.

First, let's find the total number of possible sequences. When drawing without replacement, each draw reduces the number of available balls. So for the first draw, there are 15 balls in the box (6 red + 4 white + 5 green).

When drawing the second ball, there are 14 balls left in the box because one ball has already been drawn. For the third draw, there are 13 balls left. Thus, the total number of possible sequences is 15 * 14 * 13 = 2730.

Now, let's determine the number of sequences where the balls are drawn in the order red, white, green. Since the balls must be drawn in this specific order, we multiply the number of red balls by the number of white balls and then by the number of green balls. This gives us 6 * 4 * 5 = 120.

To calculate the probability, we divide the number of desired outcomes (drawing the balls in the order red, white, green) by the total number of possible outcomes:

Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 120 / 2730
Probability ≈ 0.044 or 4.4% (rounded to one decimal place)

So, the probability that the balls are drawn in the order red, white, green is approximately 0.044 or 4.4%.