There are 4 red, N green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the sma...

Question

There are 4 red, N green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour? One cannot see the colour of the balls until they are picked.

A. 4
B. 15
C. 5
D. 2

Accepted Answer

The smallest value of N is 4. Answer: A. There are 3 colours of balls — red (4), green (N), and blue (6). We pick balls without seeing them and want the worst-case pick to still force a repeated colour. By the Pigeonhole Principle, to guarantee a repeat among k colours we need to pick k + 1 balls (one for each colour, plus one more). With 3 colours the answer is 3 + 1 = 4.

There are 4 red, N green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour? One cannot see the colour of the balls until they are picked. A. 4 B. 15 C. 5 D. 2