09_01ans - STAT 400 Fall 2011 Examples for 09/01/2011...

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STAT 400 Examples for 09/01/2011 Fall 2011 Multiplication Principle ( Fundamental Rule of Counting ): If there are n events and event i can occur in N i possible ways, then the number of ways in which the sequence of n events may occur is N 1 N 2 ... N n 1. Manager of a radio station decided that every day the broadcast will start with one of the 9 Beethoven Symphonies, followed by one of Mozart's 27 Piano Concertos, followed by one of Schubert’s 15 String Quartets. Approximately how many years can the station do that without repeating the program? 9 27 15 = 3645 days Beethoven Symphony Mozart's Piano Concerto Schubert’s String Quartet 3645 days 10 years. 1 ½ . The call letters of radio and television stations in the United States begin with either K or W. Those west of the Mississippi River start with K and those east of it with W. a) Some stations, such as KID in Idaho Falls, Idaho, and WOW in Omaha, Nebraska, have 3call letters. How many sets of call letters having 3 letters re possible? 2 × 26 × 26 = 1,352 . b) Most stations that were licensed after 1927 have 4 call letters, such as KUZZ in Bakersfield, California, and WXYZ in Detroit, Michigan. How many sets of call letters having 4 letters are possible? 2 × 26 × 26 × 26 = 35,152 . c) How many sets of call letters having 4 letters are possible if we are not allowed to repeat letters? 2 × 25 × 24 × 23 = 27,600 .
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2. In how many orders can the names of 5 candidates for the same office be listed on a ballot? 5 4 3 2 1 = 120 . 1st 2nd 3rd 4th 5th n ! = 1 2 ... ( n – 1 ) n n ! = n ( n – 1 ) ... 2 1 0 ! = 1 n ! is the number of ways to rearrange (reorder) n distinct items. For example, there are 7 ! = 5,040 different ways to arrange 7 books on a bookshelf. 3. How many ways are there of scrambling the letters of the word SCRAMBLE ? There are 8 letters in the word SCRAMBLE, none of them repeating. Therefore, there are 8 ! = 40,320 different ways to rearrange the letters. 4. Eight horses are entered in a race in which bets are placed on which horse will win, place, and show (that is, finish first, second and third). Suppose that the race is run and there are no ties. a) In how many orders can all eight horses finish the race? 8 ! = 40,320 different ways for eight horses to finish the race. b) In how many ways can the win, place, and show be taken? 8
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09_01ans - STAT 400 Fall 2011 Examples for 09/01/2011...

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