Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Can you please help me with these two questions?
(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? (Hint: See Exercise 9.2.39 with its solution in the "Read It" link,)
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Transcribed Image Text:(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? (Hint: See Exercise 9.2.39 with its solution in the "Read It" link,)
Suppose there are four routes from North Point to Boulder Creek, three routes from Boulder Creek to Beaver Dam, three routes from Beaver Dam to Star Lake, and two routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Select- Step 2: Choose a route from-Select- v to Beaver Dam. Step 3: Choose a route from Beaver Dam to Star Lake. There are choices for step 1, choices for step 2, and choices for step 3. Thus, the answer is (b) How many routes from North Point to Star Lake bypass Beaver Dam?
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Transcribed Image Text:Suppose there are four routes from North Point to Boulder Creek, three routes from Boulder Creek to Beaver Dam, three routes from Beaver Dam to Star Lake, and two routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Select- Step 2: Choose a route from-Select- v to Beaver Dam. Step 3: Choose a route from Beaver Dam to Star Lake. There are choices for step 1, choices for step 2, and choices for step 3. Thus, the answer is (b) How many routes from North Point to Star Lake bypass Beaver Dam?
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