Correct Option (B)
To guarantee picking at least one ball of each colour, the worst-case scenario must be considered. This scenario involves picking all balls of the two most numerous colours before any ball of the third colour is selected.
- The number of green balls is 8.
- The number of white balls is 7.
- The number of red balls is 5.
The two most numerous colours are green (8 balls) and white (7 balls). In the worst-case, one would pick all 8 green balls and all 7 white balls first. The total number of balls picked in this scenario would be 8 + 7 = 15 balls.
After picking these 15 balls, it is possible that no red ball has been picked. Therefore, the very next ball picked (the 16th ball) must be a red ball, thereby ensuring that at least one ball of each colour (green, white, and red) is present among the picked balls.
Incorrect Options:
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Option A (17): Picking 17 balls would certainly assure at least one of each colour, as this assurance is already met with 16 balls. Therefore, 17 is not the minimum number required.
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Option C (13): Picking 13 balls does not guarantee one of each colour. For instance, one could pick all 8 green balls and all 5 red balls (8 + 5 = 13 balls), in which case no white ball would have been picked. Alternatively, one could pick all 8 green balls and 5 white balls, missing red.
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Option D (11): Picking 11 balls is insufficient. For example, one could pick all 8 green balls and 3 white balls (8 + 3 = 11 balls), resulting in no red ball and an insufficient number of white balls to exhaust that colour, let alone guarantee all three colours.