Activity 1

 

  1. How many different ways can 10 flavors of ice cream be arranged in an ice cream store display case?
    • P(10,10) = 10! / (10-10)! = 10!/0! = 10! = 10*9*8*7*6*5*4*3*2*1
       
  2. How many different ways are there arrange 6 candidate names on a ballot?
    • P(6,6) = 6! / (6-6)! = 6!/0! = 6! = 6*5*4*3*2*1
       
  3. How many permutations of the characters in COMPUTER are there?
    • P(8,8) = 8! / (8-8)! = 8!/0! = 80! = 8*7*6*5*4*3*2*1
       
  4. How many of the permutations from problem #3 end in a vowel?
    • 3 * 7*6*5*4*3*2*1
    • There are several ways to think about this problem and I explain both in the video

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  5. How many ways can 6 people be seated in a circle of 6 chairs? Only relative positions in the circle can be distinguished.
    • The challenge in this problem is that since we are talking about relative position we don't care where person 1 sits, we only care who comes next to them.
    • So we actually begin by saying, let's just arbitrarily select person 1. Then we have to place the remaining 5.
    • P(5,5) = 5 / (5-5)! = 5!/0! = 6! = 5*4*3*2*1
    • It might confuse you that there are six different people who could be that first person. Shouldn't there be a six in there?
      • The answer is, no.
      • Because 314562 is the same ordering whether I had picked 1 first and got 145623 (they are in a circle so it "wraps") or 2 first and got 231456
         
  6. In how many ways can first, second, and third prize in a pie-baking contest be given to 15 contestants?
    • P(15,3) = 15! / (15-3)! = 15!/12! = 15*14*13
       
  7. Stock designations on the stock exchange are limited to 3 letters. How many different designations are there?
    • 26 * 26 * 26
       
  8. How many different stock designations are there if letters cannot be repeated?
    • P(26,3) = 26! / (26-3)! = 26!/23! = 26*25*24
       
  9. In how many ways can 19 people be seated in a row?
    • P(19,19) = 19! / (19-19)! = 19!/0! = 19! [I'm not writing this out]
       
  10. In how many ways can 11 men and 8 women be seated in a row?
    • For this problem, the gender of the individuals doesn't impact the decision. It's the same as #9
       
  11. In how many different ways can 11 men and 8 women be seated in a row if the men all sit together and the women all sit together?
    • P(11,11) * P(8,8) * 2 = 11! * 8! * 2