Second approach a multistep process in the first step

Info icon This preview shows pages 2–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Second approach: A multistep process. In the first step, we choose 3 out of the 10 positions to be green. In the second step, we choose 2 of the remaining 7 positions to be red. In the final step, we pick an arrangement of the 5 remaining balls in the 5 remaining positions. There are 10 3 7 2 5! = 10! 7!3! 7! 5!2! 5! = 10! 3!2! possible orderings. Third approach: A different multistep process. We first place the 5 miscel- laneous balls into 5 of the 10 positions in some order ( P (10 , 5) options). In the second step, we choose 3 of the 5 remaining positions to receive green balls ( ( 5 3 ) options). There are 2 positions left, and they will both receive red balls ( ( 2 2 ) options). There are P (10 , 5) 5 3 2 2 = 10! 5! 5! 3!2! · 1 = 10! 3!2! possible orderings. A question to see if you have the idea: 2
Image of page 2

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

View Full Document Right Arrow Icon
Question 5. A track and field team is attending a competition. There are 8 team members (all distinguishable!) and 14 events. The two team captains will participate in two events each, the other six will only participate in one each. (The team will skip four events.) How many possible arrangements are there? 3
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern