17 Section 1.2 Methods of Enumeration Students on a boat send signals back to sh

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17 Section 1.2 Methods of Enumeration Students on a boat send signals back to shore by a vertical flagpole. If they have four orange and three arranging seven colored flags on blue flags, they can send (4)- 71 4)413 a = 35 different signals. Note that if they had seven flags of different colors, they could send 7! 5,040 different signals. 1.2-1 A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number, did2dda where d , i = 1, 2, 3.4, is selected from 1.2. 3, 4, 5, 6, 7, 8. How many different lock combinations are possible with such a lock? 1.2-2 How many different signals can be made using four flags of different colors on a vertical flagpole if exactly three flags are used for each signal? 1.2-3 How many different license plates are possible if a state uses (a) Two letters followed by a four-digit integer (leading zeros permissible and the letters and digits can be repeated)? (b) Three letters followed by a three-digit integer? In designing an experiment, the researcher can often choose many different levels of the various factors in order to try to find the best combination at which to operate. For illustration, suppose the research is studying a certain chemical reaction and can choose four levels of temperature, five different pressures, and two different catalysts. (a) To consider all possible combinations, how many experiments would need to be 124 conducted? (b) Often in preliminary experimentation, each factor is restricted to two levels With the three factors noted, how many experiments would need to be run to cover all possible combinations with each of the three factors at two levels? (NoTE: This is often called a 2' design.) 1.2-5 Some albatrosses return to the world's only mainland colony of royal albatrosses on Otago Peninsula nea their young. In order to learn more about the albatross, colored plastic bands are placed on their legs so that they can ban and blue. Find the number of different color codes that are albatross if be identified from a distance. Suppose that three ced on one leg, selecting from the colors red, yellow, green, white, possible for banding an pla (a) The three bands are different colors (b) Repeated colors are permissibl that Andy Roddick and Roger Federer are playing a tennis match in

Explanation / Answer

Answer:

2-1

There are 4 digits( positions) in the lock.

For each position there are 8 possible numbers( 1 to 8).

The possible lock combinations are 8*8*8*8 = 4096.

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