Answer:
we will select 9 balls to be sure of having at least five balls of the same color.
Step-by-step explanation:
Given that:
The bowl contains (20 red + 20 blue) balls = 40 balls
If we are to select 5 balls out of the 40 balls.
Let R = red and B = blue
The combinations can be:
5R + 0 B
4R + 1 B
3R + 2 B
1R + 4 B
0 R + 5 B
From above, we will notice that there are valid proof that there are 5 balls of the same color.
If we select six balls, we have:
= (6R + 0 B ), (5R + 1 B ), (4R + 2 B ), (3R + 3 B ), (2R + 4 B ), (1R + 5 B ), (0R + 6 B )
If we select seven balls, we have:
= (7R + 0 B ), (6R + 1 B ), (5R + 2 B ), (4R + 3 B ), (3R + 4 B ), (2R + 5 B ), (1R + 6 B ), (0R + 6 B ).
If we select eight balls, we have:
= (8R + 0 B ), (7R + 1 B ), (6R + 2 B ), (5R + 3 B ), (4R + 4 B ), (3R + 5 B ), (2R + 6 B ), (1R + 7 B ), (0R + 8B)
Now, selecting nine balls, we have the following combinations:
= (9R + 0 B ), (8R + 1 B ), (7R + 2 B ), (6R + 3 B ), (5R + 4 B ), (4R + 5 B ), (3R + 6 B ), (2R + 7 B ), (1R + 8B), (0R + 9B).
Thus, we can see that all the combinations comprise of 5 balls with at least one color.
Therefore, we will select 9 balls to be sure of having at least five balls of the same color.
