HW3_Sol

# HW3_Sol - Problem 8 Solution (a) Since the cars are all...

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Problem 8 Solution (a) Since the cars are all distinct, there are 20! ways to line them up. (b) To find the probability that the cars will be parked so that they alternate, we count the number of “favorable” outcomes, and divide by the total number of possible outcomes found in part (a). We count in the following manner. We first arrange the US cars in an ordered sequence (permutation). We can do this in 10! ways, since there are 10 distinct cars. Similarly, arrange the foreign cars in an ordered sequence, which can also be done in 10! ways. Finally, interleave the two sequences. This can be done in two different ways, since we can let the first car be either US-made or foreign. Thus, we have a total of 2 · 10! · 10! possibilities, and the desired probability is ± ² ±³´µ±² ±³´µ ´µ Note that we could have solved the second part of the problem by neglecting the fact that the cars are distinct. Suppose the foreign cars are indistinguishable, and also that the US cars are indistinguishable. Out of the 20 available spaces, we need to choose 10 spaces in which to place

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## This note was uploaded on 02/11/2012 for the course EEE 352 taught by Professor Ferry during the Spring '08 term at ASU.

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HW3_Sol - Problem 8 Solution (a) Since the cars are all...

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