Five red balls and seven green balls are placed in a bag. Each ball is unique. A person selects 5 balls from the bag. What is the probability that all 5 balls are red?
A) 1 B) 1/792 (This is a fraction) C) 1/396 (This is a fraction)
5/12 * 4/11 * 3/10 * 2/9 * 1/8
To find the probability that all 5 balls selected are red, we need to calculate the number of favorable outcomes (selecting all red balls) divided by the number of possible outcomes (selecting any 5 balls).
First, let's determine the total number of possible outcomes. Since there are 12 balls in total (5 red and 7 green), and we are selecting 5 balls, we can use the combination formula to find the number of possible outcomes:
Total number of possible outcomes = C(12, 5) = 12! / (5!(12 - 5)!) = 792
Next, let's determine the number of favorable outcomes, which is when all 5 selected balls are red. Since there are only 5 red balls in the bag, there is only one possible combination where all 5 selected balls are red.
Number of favorable outcomes = 1
Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 1 / 792
Therefore, the answer is B) 1/792.