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A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking atleast one ball of each colour?

a) 15 

b) 16

c) 17

d)18

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3 Answers

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Consider Three buckets Green White and Red and we want the total no of balls such that each bucket contain atleast one ball.
Now consider the scenario of picking up a ball without replacement :

(normally you consider the worst case scenario in these cases)

Starting 8 balls all are green and thus goes to bucket name Green.

Now you again started picking up the ball and you find that 7 are of same colour you put all of them in bucket named White.

The next pick will definetly be of different colour thus : you picked 8+7+1=16.

Other way to think about it :

There are 8 balls that are green and 7 that are white.Now,if we pick 8 + 7 = 15 balls,there remains a chance that 8/8 are green and 7/7 are white,that is all 15 are green and white.Now,if we pick 15+1 = 16 balls,there cannot be more than 15 balls that are green and white,so we will get at least 1 red ball.
1 votes
1 votes
for getting at least one ball of every color in worst case you have to get all 8 green balls, and 7 white balls and after that you can pick just one ball from the bag after all these drawn then that ball will be definitely of red color, So, in this way you satisfy the condition for at least one ball of all color.

so 8 + 7 + 1 = 16,

and this is the minimum no of balls in order to be 100% sure that picked up balls contain all three colors.

if you pick less than 16 then it is not guaranteed that you will satisfy the condition, suppose you picked15 balls there may be a chance of getting 8 green and +7 white ball, and in this combination, you don't have a white ball which dis-satisfying the condition.

hence minimum is 16 only.
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0 votes
lets think like an aptitude question

bag contain 8 balls=g ,7=w ,5=r

you have picked 8 balls

now i am saying there will be a chance of 8 balls of same colour bz bag holding 8 balls of same color

now if you pick one more ball

then this ball definitely will be from other two color

now after picking 8 balls choose next maximum (i.e.7)

pick 7 balls

now again i say 15 balls you picked are only of green and white

but if you picked one ball more then there will definitely one ball which is not same as previous balls(these instances are the worst cases).

Hope you get, if(not) tRy pigeonhole principle

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