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Sagot :
We have to use pigeonhole principle to find balls from bowl. For each color to be found at least once we have to calculate it case by case.
out of 75 balls for each ball to be chosen at least once then we have to compute each color of ball separately,
By using the pigeonhole principle's formula n(r - 1) + 1
For red ball,
N=11, k=1, [N/2]≥3
= 11(3-1)+1
= 23
Hence, out of 23 balls from 75 balls at least one will be of red color
For, blue ball
N=12, k=1, [N/2]≥3
= 12(3-1)+1
= 25
Hence, out of 25 balls from 75 balls at least one will be of blue color
For green color,
N=13, k=1, [N/2]≥3
= 13(3-1)+1
= 27
Hence, out of 27 balls from 75 balls at least one will be of green color
For yellow ball,
N=14, k=1, [N/2]≥3
= 14(3-1)+1
= 29
Hence, out of 29 balls from 75 balls at least one will be of yellow color
For black ball,
N=15, k=1, [N/2]≥3
= 15(3-1)+1
= 31
Hence, out of 31 balls from 75 balls at least one will be of black color
The pigeonhole principle states that if n items are put into m containers, where n > m, at least one container must contain more than one item. If there are k+1 or more pigeons dispersed throughout the k pigeonholes, at least one pigeonhole will have two or more pigeons. Proof. The statement's converse is that there can only be a maximum of k pigeons if each slot can only accommodate one bird.
To learn more about pigeonhole principle: https://brainly.com/question/13982786
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