# problems09-sol - MATH S-104 Lecture 9 In-class Problem...

This preview shows pages 1–2. Sign up to view the full content.

MATH S-104 Lecture 9 In-class Problem Solutions July 21, 2009 Problem 1 * : a) How many possibilities are there for the win, place and show (first, second and third) positions in a horse race with 12 horses if all orders of finish are possible? P ( 12 , 3 ) = 12! 9! = 12 11 10 = 1320 . b) How many di ff erent sets of three horses can win a place on the podium (that is, first, second or third place)? For this one, we don’t care about the order of the horses. C ( 12 , 3 ) = 12! 3!9! = 12 11 10 3! = 220. c) How many possible results are there for the entire field? There are P ( 12 , 12 ) = 12! = 479 , 001 , 600 ways to order the 12 horses. d) How many possible results are there where the favorite wins a place on the podium? There are 11! possibilities for each of the possible finishes, so there are 3 11! = 11 , 9750 , 400 possibilities. e) If only the first six horses go on to the next race, how many possible sets of horses go on to the next race? C ( 12 , 6 ) = 12! 6!6! = 12 11 10 9 8 7 6! = 924. Problem 2 : b) How many distinguishable orderings of the letters of HULLABALOO begin with U and end with L ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern