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Combinatorics Problem Set 1: Soham Bakshi September 2020

The document is a combinatorics problem set containing 7 questions: 1) It asks how many ways Sayantana and Ritabrata can exchange 3 books when Sayantana has 6 books and Ritabrata has 8 books. 2) It asks how many ways a coach can choose a team of 4, with at least 1 girl, from a chess club with 2 girls and 7 boys. 3) It asks how many ways 10 boys can be divided into 2 basketball teams of 5 boys each. The summary provides a high-level overview of the type and number of problems in the document in 3 sentences.

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60 views1 page

Combinatorics Problem Set 1: Soham Bakshi September 2020

The document is a combinatorics problem set containing 7 questions: 1) It asks how many ways Sayantana and Ritabrata can exchange 3 books when Sayantana has 6 books and Ritabrata has 8 books. 2) It asks how many ways a coach can choose a team of 4, with at least 1 girl, from a chess club with 2 girls and 7 boys. 3) It asks how many ways 10 boys can be divided into 2 basketball teams of 5 boys each. The summary provides a high-level overview of the type and number of problems in the document in 3 sentences.

Uploaded by

ydyane3d
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Combinatorics Problem Set 1

Soham Bakshi
September 2020

1. Sayantana has 6 math books and Ritabrata has 8 books. How many ways
they can exchange 3 books with each other?

2. There are 2 girls and 7 boys in a chess club. How many ways the couch can
choose a team of 4 with at least 1 girl member for a tournament?

3. How many ways can you divide 10 boys into 2 basketball teams of 5 boys
each?

n n
 
4. Prove that k = n−k . (try to get the intuition)

5. Suha has 6 friends. Each evening, for 5 days, she invites 3 of them so that
the same group is never invited twice. How many ways are there to do this?

6. Let S = {1, 2, . . . , 10}. How many subsets are there of S containing exactly 5
elements? How many subsets are there of S containing even number of elements?
How many subsets are there in total of S?

7. How many neckless can be made using 5 identical red beans and 2 identical
blue beans?

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