TIFR CSE 2021 | Part A | Question: 1

Question

A box contains $5$ red marbles, $8$ green marbles, $11$ blue marbles, and $15$ yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least $7$ are of the same colour?

• A. $7$
• B. $8$
• C. $23$
• D. $24$
• E. $39$

Answer 1

Consider the worst case scenario. We have 6 each of different colours(but note that there are only 5 red ones).

Therefore pick $5(red)+6(green)+6(blue)+6(yellow)=23$.

Now adding one more marble ensures that we have at least 7 of the same colour (By pigeonhole principle).

Threrefore, $\mathbf{23+1=24 }$

Option (D)