<PRE><B>Question 188327</B>
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.
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