## mathmath333 one year ago A box contains five set of balls while there are three balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{A box contains five set of balls while there are three balls in each set.}\hspace{.33em}\\~\\ & \normalsize \text{Each set of balls has one colour which is different from every other set.}\hspace{.33em}\\~\\ & \normalsize \text{What is the least number of balls that must be removed from the box in }\hspace{.33em}\\~\\ & \normalsize \text{order to claim with certainty that a pair of balls of the same colour has }\hspace{.33em}\\~\\ & \normalsize \text{been removed.}\hspace{.33em}\\~\\ \end{align}}

2. mathmath333

\large \color{black}{\begin{align} & a.)\ 6 \hspace{.33em}\\~\\ & b.)\ 7 \hspace{.33em}\\~\\ & c.)\ 9 \hspace{.33em}\\~\\ & d.)\ 11 \hspace{.33em}\\~\\ \end{align}}

3. mathmath333

i am not even able to interpret the question

4. hartnn

wouldn't it just be 6?? think of the best case!

5. anonymous

condition on the color...

6. hartnn

you draw 5 balls from 5 different sets. whichever ball you choose next, will repeat the color

7. mathmath333

answer given in book is d.) 11

8. hartnn

trust on yourself more than the book :)

9. anonymous

"Each set of balls has one colour which is different from every other set." meaning all of the balls in a set have the same color and that the color of each set is distinct? is this english class or probability?

10. ganeshie8

imagine you have 10 black balls and 5 other balls have different colors |dw:1441043358114:dw|

11. mathmath333

ok

12. anonymous

question is poorly phrased

13. anonymous

... if the answer is indeed 11

14. ganeshie8

if you put ur hand inside the box and randomly take one ball, there is a chance that you get a black ball, yes ?

15. mathmath333

yes

16. ganeshie8

throw away that black ball next, put ur hand in box and take out one ball again there is a chance that you get a black ball again, yes ?

17. mathmath333

yes there is

18. ganeshie8

why no there are still 9 more black balls in the box

19. mathmath333

yes there is a chance.

20. ganeshie8

if you take out 10 balls, it can so happen that you get all 10 black balls, yes ?

21. ganeshie8

but if you take out 11 balls, can you be certain that at least one ball is different from black ?

22. mathmath333

yes

23. mathmath333

yes

24. ganeshie8

if you're clever enough, you could also use pigeon hole principle and work it more formally

25. mathmath333

what is the meaning of this line , Each set of balls has one colour which is different from every other set

26. ganeshie8

|dw:1441043775878:dw|

27. ganeshie8

look at above partition of 15 balls in the box notice that there are 5 groups each group has at least one ball whose color is different from the colors of balls in all other sets

28. ganeshie8

the wording in the question is indeed confusing i have just cooked up the solution to match the answer by reverse engineering sortof..

29. mathmath333

yes thnks

30. ganeshie8

they wont ask such poorly phrased questions in real tests usually you see them only in practice problems cooked up by careless authors

31. mathmath333

yes i don't think this can be solve in 1 or 3 minutes with time pressure , 1 hour will be wasted only to understand the question

32. ganeshie8

Exactly, if you understand the question correctly, then i think its not hard to approach it