Quiz8Soln

# Quiz8Soln - alphabet Out of 26 letters four are to be...

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Math 17C, Spring 2009 Instructor: Timothy Lewis TA: Tamara Schlichter (Section A01) QUIZ 8 - SOLUTIONS Name: Student ID: Show all work for credit. 20 pts possible. 1. (6 pts) Suppose that you want to investigate the inﬂuence of light and fertilizer levels on plant performance. You plan to use ﬁve fertilizer and two light levels. For each combination of fertilizer and light level, you want four replicates. What is the total number of replicates? One experiment (trial) consists of using one fertilizer with one light level. There are 5 diﬀerent fertilizers and each is to be tested with every one of the two light levels. Thus one has to conduct 5 · 2=10 trials. But each trial is required to have 4 replicates. Hence the total number of replicates is given by 5 · 2 · 4=40. 2. (7 pts) How many four-letter words with no repeated letters can you form from the 26 letters of the
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Unformatted text preview: alphabet? Out of 26 letters, four are to be chosen at a time. Remember that the order is very important, since each order stands for a diﬀerent word. This is a clear case for using permutation. Hence the number of words that can be formed in this case is P (26 , 4). This is equal to 26! / 22!, which is 23 · 24 · 25 · 26. So the number of words is a phenomenal 358,800. 3. (7 pts) An urn contains 15 diﬀerent balls. In how many ways can you select four balls without replacement? Four balls can be selected out of ﬁfteen balls in C (15 , 4) ways. Applying the formula for combinations, 15! ÷ (4! · 11!) = 12 · 13 · 14 · 15 ÷ (2 · 3 · 4)=1365 ways....
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