Final answer:
The probability of selecting 5 green balls at random, without replacement, from a bag containing 3 red and 7 green balls is 1/12.
Step-by-step explanation:
The question asks to determine the probability of selecting 5 green balls from a bag containing 3 red balls and 7 green balls, without replacement. The probability is calculated using combinations. First, we need to find the number of ways to select 5 green balls from the 7 available, which is given by the combination formula C(7,5). Next, we calculate the total number of ways to select 5 balls from all the 10 balls in the bag, which is given by C(10,5). The probability of selecting 5 green balls without replacement is then the ratio of these two combinations: P(5 green) = C(7,5) / C(10,5).
The combinations are calculated as follows: C(n, r) = n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and ! denotes factorial. Therefore, C(7,5) = 7! / (5!(7-5)!) = 21 and C(10,5) = 10! / (5!(10-5)!) = 252. The probability is thus P(5 green) = 21 / 252 = 1/12.