Question

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

Answer 1

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

Answer 2

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

\end{align}}\)

Answer 3

i am not even able to interpret the question

Answer 4

wouldn't it just be 6??

think of the best case!

Answer 5

condition on the color...

Answer 6

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

Answer 7

answer given in book is d.) 11

Answer 8

trust on yourself more than the book :)

Answer 9

"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?

Answer 10

imagine you have 10 black balls
and 5 other balls have different colors

Answer 11

ok

Answer 12

question is poorly phrased

Answer 13

... if the answer is indeed 11

Answer 14

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

Answer 15

yes

Answer 16

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 ?

Answer 17

yes there is

Answer 18

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

Answer 19

yes there is a chance.

Answer 20

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

Answer 21

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

Answer 22

yes

Answer 23

yes

Answer 24

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

Answer 25

what is the meaning of this line ,

Each set of balls has one colour which is different from every other set

Answer 26

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

Answer 27

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

Answer 28

yes thnks

Answer 29

they wont ask such poorly phrased questions in real tests

usually you see them only in practice problems cooked up by careless authors

Answer 30

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

Answer 31

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