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Quiz-5

Page history last edited by Scott Staley 14 years, 10 months ago

This quiz tests your understanding of ...

Multiplication Principle, Permutations, & Combinations 

(Key: correct, incorrect, partially correct.)

 

  1. One of the State of Indiana's license plate has three numbers followed by three letters. How many plates are possible?
    1. 3! * 3! = 36
      • INCORRECT.
    2. 10 * 9 * 8 * 26 * 25 * 24 = 11,232,000
      • Not quite. This would be correct if it was stated that the numbers and letters can not be repeated.
    3. 10! * 10! * 10! * 26! * 26! * 26!
    4. 10 * 10 * 10 * 26 * 26 * 26 = 17,576,000
      • CORRECT.
    5. None of these.
  2. How many 6-letter words can be formed from the letters in the word "FINITE"?
    1. 6! = 120
    2. 6!/2! = 360
    3. 4! * 2! = 48
    4. 5 + 4 + 3 + 2 + 1 = 15
    5. None of these.
  3. At a local high school the lockers have combination locks with forty numbers on them. For a student to open one, he/she needs to turn counterclockwise two full rotations to the first number, then a clockwise rotation is needed to get to the second number, and then lastly counterclockwise to the final number. How many different locker combinations are there?
    1. 40* 39 * 38 = 59,280
    2. 40 + 40 + 40 = 120
    3. 40 * 40 * 40 = 64,000     
    4. 40!
    5. None of these.
  1. A high school math department has fourteen teachers. Each teacher has to be on one and only one committee. The Algebra I committee needs 5 teachers. The Geometry committee needs 4 teachers. The Algebra II committee needs 3 teachers. And thePre-Calculus committee needs 2 teachers. How many committees can be formed?
    1. C ( 14, 5 ) + C ( 9, 4 ) + C ( 5, 3) + C ( 2, 2) = 2,002 + 126 + 10 + 1 = 2,139
    2. C ( 14, 5 ) * C ( 9, 4 ) * C ( 5, 3) * C ( 2, 2) = 2,522,520
    3. P ( 14, 5 ) + P ( 9, 4 ) + P ( 5, 3) + P ( 2, 2) = 240,240 + 3,024 + 60 + 2 = 243,326
    4. P ( 14, 5 ) * P ( 9, 4 ) * P ( 5, 3) * P ( 2, 2) = 87,178,291,200
    5. None of these.
  2. How many 5-card poker hands contain exactly 3 queens?
    1. C( 4, 3 ) + C ( 48, 2 ) =4 + 1128 = 1132
    2. C( 4, 3 ) * C ( 48, 2 ) = 4 * 1128 = 4512
      • CORRECT.
    3. P ( 4, 3 ) * P ( 48, 2 ) = 24 * 2256 = 54,144
    4. P ( 4, 3 ) + P ( 48, 2 ) = 24 + 2256 = 2280
    5. None of these

 

 

 

 

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