Mathematics
Problem of The Day
2023
26

26

There are 28 red, 20 green, 12 yellow, 20 blue, 10 white and 10 black balls in a box.

How many balls need to be randomly drawn from the box, without peeking, to ensure that at least 15 balls of the same color are among those drawn?

Answer

75 balls

SOLUTIOn

To ensure at least 15 balls of the same colour, we consider the worst-case scenario:

Draw 14 red, 14 green, 12 yellow, 14 blue, 10 white, and 10 black balls, which totals 74 balls without getting 15 of any colour.

The next ball (75th) will make one colour reach 15.

Thus, the minimum number of balls needed is 75 balls.

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