ProbabilityA bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:Options1/311/342/911/92

To solve this problem, we need to use the concept of combinations in probability.

Step 1: Find the total number of balls in the bag. There are 4 white balls, 5 red balls, and 6 blue balls. So, the total number of balls is 4 + 5 + 6 = 15 balls.

Step 2: Find the total number of ways to draw 3 balls from 15. This is a combination problem, which can be solved using the formula for combinations: nCr = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, the total number of ways to draw 3 balls from 15 is 15C3 = 15! / [(15-3)! * 3!] = 455 ways.

Step 3: Find the total number of ways to draw 3 red balls from 5. Again, this is a combination problem. So, the total number of ways to draw 3 red balls from 5 is 5C3 = 5! / [(5-3)! * 3!] = 10 ways.

Step 4: Find the probability that all three balls drawn are red. The probability is the number of favorable outcomes (drawing 3 red balls) divided by the total number of outcomes (drawing any 3 balls). So, the probability is 10 / 455 = 2/91.

Therefore, the probability that all three balls drawn are red is 2/91. So, the correct option is 2/91.