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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

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{A box contains five set of balls while there are three balls in each set.}\hspace{.33em}\\~\\ & \normalsize \text{Each set of balls has one colour which is different from every other set.}\hspace{.33em}\\~\\ & \normalsize \text{What is the least number of balls that must be removed from the box in }\hspace{.33em}\\~\\ & \normalsize \text{order to claim with certainty that a pair of balls of the same colour has }\hspace{.33em}\\~\\ & \normalsize \text{been removed.}\hspace{.33em}\\~\\ \end{align}}\)

  2. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & a.)\ 6 \hspace{.33em}\\~\\ & b.)\ 7 \hspace{.33em}\\~\\ & c.)\ 9 \hspace{.33em}\\~\\ & d.)\ 11 \hspace{.33em}\\~\\ \end{align}}\)

  3. mathmath333
    • one year ago
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    i am not even able to interpret the question

  4. hartnn
    • one year ago
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    wouldn't it just be 6?? think of the best case!

  5. anonymous
    • one year ago
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    condition on the color...

  6. hartnn
    • one year ago
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    you draw 5 balls from 5 different sets. whichever ball you choose next, will repeat the color

  7. mathmath333
    • one year ago
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    answer given in book is d.) 11

  8. hartnn
    • one year ago
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    trust on yourself more than the book :)

  9. anonymous
    • one year ago
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    "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
    • one year ago
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    imagine you have 10 black balls and 5 other balls have different colors |dw:1441043358114:dw|

  11. mathmath333
    • one year ago
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    ok

  12. anonymous
    • one year ago
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    question is poorly phrased

  13. anonymous
    • one year ago
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    ... if the answer is indeed 11

  14. ganeshie8
    • one year ago
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    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
    • one year ago
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    yes

  16. ganeshie8
    • one year ago
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    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
    • one year ago
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    yes there is

  18. ganeshie8
    • one year ago
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    why no there are still 9 more black balls in the box

  19. mathmath333
    • one year ago
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    yes there is a chance.

  20. ganeshie8
    • one year ago
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    if you take out 10 balls, it can so happen that you get all 10 black balls, yes ?

  21. ganeshie8
    • one year ago
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    but if you take out 11 balls, can you be certain that at least one ball is different from black ?

  22. mathmath333
    • one year ago
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    yes

  23. mathmath333
    • one year ago
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    yes

  24. ganeshie8
    • one year ago
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    if you're clever enough, you could also use pigeon hole principle and work it more formally

  25. mathmath333
    • one year ago
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    what is the meaning of this line , Each set of balls has one colour which is different from every other set

  26. ganeshie8
    • one year ago
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    |dw:1441043775878:dw|

  27. ganeshie8
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yes thnks

  30. ganeshie8
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Exactly, if you understand the question correctly, then i think its not hard to approach it

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