Question 3 Suppose you place 3 red poker chips on a 5x5 grid, with no two...

 

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Question 3 Suppose you place 3 red poker chips on a 5x5 grid, with no two chips sharing a space on the grid. Assume that the position of the grid itself is fixed-you cannot rotate it. (a) How many distinguishable configurations are there for the 3 red chips? If you take a configuration and swap two red chips, these are not distinguishable. (b) If the 3 red chips are placed randomly, what is the probability that they are placed in a straight horizontal or vertical line (diagonal lines don't count)? Note that 3 chips are considered to be in a straight line if they are in the same row or column of the grid, even if there are spaces between them. (c) Now suppose you place 3 different colored poker chips (yellow, green, and blue) on the 5x5 grid. How many distinguishable configurations are there for the 3 colored chips? Note that if you swap two of the chips, these are distinguishable. (d) If the 3 (yellow, green, and blue) chips are placed randomly, what is the probability that they are placed in a straight horizontal or vertical line? Question 3 Suppose you place 3 red poker chips on a 5x5 grid, with no two chips sharing a space on the grid. Assume that the position of the grid itself is fixed-you cannot rotate it. (a) How many distinguishable configurations are there for the 3 red chips? If you take a configuration and swap two red chips, these are not distinguishable. (b) If the 3 red chips are placed randomly, what is the probability that they are placed in a straight horizontal or vertical line (diagonal lines don't count)? Note that 3 chips are considered to be in a straight line if they are in the same row or column of the grid, even if there are spaces between them. (c) Now suppose you place 3 different colored poker chips (yellow, green, and blue) on the 5x5 grid. How many distinguishable configurations are there for the 3 colored chips? Note that if you swap two of the chips, these are distinguishable. (d) If the 3 (yellow, green, and blue) chips are placed randomly, what is the probability that they are placed in a straight horizontal or vertical line?

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The image contains a problem statement broken down into four parts a to d regarding the placement of poker chips on a 5x5 grid Here Ill respond to each part a How many distinguishable configurations a... View the full answer