SOLUTION: Suppose you have a 10 by 10 checkerboard with alternating brown and white squares. If 5 pieces are randomly placed on the checkerboard. What is the probability that they will all

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Question 188327: Suppose you have a 10 by 10 checkerboard with alternating brown and white squares. If 5 pieces are randomly placed on the checkerboard.
What is the probability that they will all be in the column #1?
What is the probability that they will all be in the same column?
What is the probability that they will all be placed on white squares?
What is the probability that they will all be placed on squares of the same color?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose you have a 10 by 10 checkerboard with alternating brown and white squares. If 5 pieces are randomly placed on the checkerboard.
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What is the probability that they will all be in the column #1?
# of ways to place 5 pieces in the 1st column: 10C5
# of ways to place 5 pieces on the 100 spaces: 100C5
Ans: 10C5/100C5 = 252/75287520 = 0.000003347..
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What is the probability that they will all be in the same column?
Ans: 10 times the answer to the previous question.
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What is the probability that they will all be placed on white squares?
# of ways to place 5 pieces on 50 white: 50C5
# of ways to place 5 pieces on 100 spaces: 100C5
Ans: 50C5/100C5 = 0.0281
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What is the probability that they will all be placed on squares of the same color?
# of ways to pick a color: 2
Ans: 2 times the answer to the previous question = 0.0563
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If you know a better way to answer the questions you should
use it.
Cheers,
Stan H.