There are total 18 balls in a bag. Out of them 6 are red in colour, 4 are green in colour and 8 are blue in colour. If vishal picks three balls randomly from the bag, then what will be the probability that all the three balls are not of the same colour?

To solve this problem, we first need to calculate the total number of ways to draw 3 balls from 18, which is a combination problem. The formula for combinations is 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.

Step 1: Calculate total number of ways to draw 3 balls from 18 Using the combination formula, we get C(18, 3) = 18! / [3!(18-3)!] = 816.

Step 2: Calculate the number of ways to draw 3 balls of the same color For red balls, it's C(6, 3) = 6! / [3!(6-3)!] = 20. For green balls, it's C(4, 3) = 4! / [3!(4-3)!] = 4. For blue balls, it's C(8, 3) = 8! / [3!(8-3)!] = 56. So, the total number of ways to draw 3 balls of the same color is 20 + 4 + 56 = 80.

Step 3: Calculate the number of ways to draw 3 balls that are not of the same color This is simply the total number of ways to draw 3 balls minus the number of ways to draw 3 balls of the same color. So, it's 816 - 80 = 736.

Step 4: Calculate the probability The probability is the number of ways to draw 3 balls that are not of the same color divided by the total number of ways to draw 3 balls. So, it's 736 / 816 = 0.902.

So, the probability that all the three balls are not of the same color is approximately 0.902 or 90.2%.