{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam2_301

# Exam2_301 - Permutation P(n,r)=r-permutation of n distinct...

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

Permutation: P(n,r)=r-permutation of n distinct objects is an arrangement using r of the n objects. ORDER MATTERS: P(n,r) = n!/(n-r)! Combination: C(n,r) A r-combination of n distinct objects is an unordered selection of r out of n objects. C(n,r) =n!/{(n-r)!r!) C(n,r)=C(n,n-r) P(n,r)=C(n,r)*r! How many ways are there to form a sequence of 10 letters from 4as, 4bs, 4cs, and 4ds if each letter must appear at least twice? Aa bb cc dd aa 4 cases P(10; 4, 2, 2, 2) = 18,900 limited repetition + ordered aa bb cc dd ab C(4,2) have 4 letter choose 2diff =6 cases P(10; 3, 3, 2, 2) = 25,200 = we have 10 total letter, 3 of 2 types of letter, 2 of 2 other types limited repetition + ordered A: 4 ×18,900+ 6×25,200 = 226,800 How many ways are there to pick exactly 10 balls from a pile of red, blue and purple balls, if there must be at most 5 red balls? 10 balls from 3 types c(10+3-1,10)=66 At least 6=At most 5 . At least 6 is C(4+3-1,4) This is the leftover 3=types 1 in formula, 4 is leftover balls. Six cups of diff flavor ice cream: Distribute to 3 kids: r distinct objects to 3 kids: n^r Distribute with restriction, 2 to J, 3toM 1 to Rose: P(r:r1,r2,rn) ri objects go in box i. Distribute 6 cups of identical object to 3 things: C(r+n-1, r)= (r+n-1)!/r!(n-1)! *How manyways if 20 diplomats must be assigned to each country.100 total diff diplomats 5 countries: Distinct distribution with repetition: P(100:20,20,20,20,20) 20 for 5 country , 100 total distinct items(diplomats):::*Bridge,

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