Math 326                                                                                                                 Name______KEY__________
Quiz 2
  1. How many different ways are there to arrange the letters in the word "pencil"?

    2.  
        6! (Arrangement of 6 distinct elements.)
         
  2. How many different ways are there to arrange the letters in the word "banana"?

    3.  
        (Arrangement of 6 elements with a group of 3 that are the same (a’s) and a group of 2 that are the same (n’s). See the formula on P. 457)
         
  3. How many different codes are there that consist of a letter (A- Z) followed by two digits (0- 9) followed by another letter and then ending with either a 7 or an 8 (Examples: A93R7, X05X8)?

    4.  
        (letter, digit, digit, letter, 7 or 8)

     
  4. Assume you have to form a committee of 7 people out of a group of 45. How many different committees is it possible to make assuming that all committee positions are the same?

    5.  
        (This is a combination, because all the positions are the same (order doesn’t matter).)
         
  5. Assume that you are planning a play about animals. 75 people turn up to audition for any part in the play. The roles in the play are Bear, Owl, Tiger, Elephant, and Swan. How many different casts is it possible to make out of the 75 people that audition?

    6.  
        (This is a permutation, because the roles are not the same (order matters).)

     
  6. (Review) Suppose the names of the days of the week (Sunday- Saturday) are put in a bag and you draw one of the names at random. You then put that name back and draw another name from the bag. What is the probability that the two days drawn are Tuesday and Thursday (in either order)?
 
 
So,