# hwk2 - Solutions to Homework 2 2.41 10 There are ways to...

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Solutions to Homework 2 2.41 There are ways to choose 4 engineers out of 10, a nd there are 4!ways to assign 4 different positions to 4 engineers chosen, thus 10 4    There are ways can the director fill the positions. 10 4! 5040 4  2.50 For each of the 10 questions, sh e has two choices, tru e and false. Thus, there are ways for the student to finish the test . Because she is guessing, each way has the same probability. 10 2 If she gets exactly i correct, there are ways to specify i correct in 10 questions. 10 i To pass the test, the student need exactly 7 or 8 or 9 or 10 correct, there are ways to pass the test. 10 10 10 10 789 1 0     Therefore, the probability of passing the test is 10 10 10 10 10 1 0 11 26 4 2.62 There are ways to arrange 4 men with order, and there are ways to arrange 4 women with order, thus there are 4 4 4! P 4! 4! 576 4! 24 ways for the waiter to seat four couples. If four couples are seated across from one another, after we specify the m en’s seats, women’s seats are fixe d, thus th ere are possible outcomes that couples are all seated across from each other, the probability is 24 1 576 24 2.68 First we need to know the total number of pa tterns in a system of 8 particles and 10 phase cells. Cells are distingu ishable, we can denote them by cellone, celltwo, …, cellten. Each distribution of particles am ong phase cells can b e seen as on e outcom e of selecting 8 cells out of 10 cells with repl acement and without order . If one cell is

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selected times, we assign particles to this cell. i i For example, one outcome of selecting 8 cells out of 10 cells is: 3 cellone, 2 celltwo, 3 cellten. Then we assign 3 pa rticles to ce llone, 2 partic les to celltw o, 3 particles to cellten, this is a distribution of 8 particles among 10 phase cells. Therefore, there are distributions of 8 particles a mong 10 phase cells.
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## This note was uploaded on 02/14/2012 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

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hwk2 - Solutions to Homework 2 2.41 10 There are ways to...

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