Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Exam 1 with Solved Problems - Combinatorics Type | MATH 172, Exams of Mathematics

University of California - BerkeleyMathematics
Prof. M. Haiman

Material Type: Exam; Professor: Haiman; Class: COMBINATORICS; Subject: Mathematics; University: University of California - Berkeley; Term: Spring 2010;

Typology: Exams

2010/2011

Uploaded on 05/11/2011

koofers-user-1hy
koofers-user-1hy 🇺🇸

9 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
pf3

Partial preview of the text

Download Exam 1 with Solved Problems - Combinatorics Type | MATH 172 and more Exams Mathematics in PDF only on Docsity!

1. (10 points each) For each of the following counting problems, express the answer in terms of factorials, falling powers, binomial, multinomial and multichoose coefficients, Stir- ling numbers (of either kind) and/or partition numbers. Write answers in an unsimplified form which suggests how you derived them. No further explanation in words is required. (a) Find the number of compositions of the integer 50 into 4 parts, in which each part is greater than or equal to 5. (A> (EB) # (3) " Zo? So-rds (b) Find the number of rearrangements of the letters in the word REARRANGING. 44 (5 2,2,2, 44 (c) Find the number of partitions of the set {1,2,...,10} into 5 blocks, with the property that 1 and 10 are in different blocks. $(10,¢) - $€3,5) t Ut aud 10 ae wm te Sue block Ue Com tread then as f they were a tiugh elowoct .