### Discrete Mathematics Week 1

**Discrete Mathematics Week 1 Assignment 1 Answers**

Course link: https://onlinecourses.nptel.ac.in/noc22_cs123/course

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In how many ways the word ‘PATHOGEN’ can be arranged such that letter O always comes to the left of K.

5040

40320**20160**10080

*CREDIT : ADITYA POKRA*

*EXPLANATION : There’s an error in question but whatever letter you put from ‘PATHGON’ to the left of ‘O’ you will always get an answer = 20160.*

Rahul has 7 differently colored shirts, 5 different jeans, 2 pairs of shoes and 3 different caps. In how many ways can Rahul dress up before going to a party?

105

17**210**

41

In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together?

6!/2!×13!/(2!×2!×2!)

13!/(2!×2!×2!)

7!/(2!×2!)

**6!/2!×7!/(2!×2!)**

A question paper consists of 20 questions, having 2 parts. Each part consists of 10 questions. Students have to answer 12 questions in total, of which at least 4 questions should be from part 1 and at least 4 questions from part 2. In how many ways can the student select questions?

44100

9450**123480**

40320

What is the coefficient of the 6th term in the expression (5x^4/13−x^3/2)^7

−4375/35152

**−525/5408**

−35/832

−375/2704

Which of the following is NOT an application of catalan numbers?

Counting the number of ways in which a polygon can be cut into triangles by connecting vertices by straight lines.**Counting the number of ways in which a person can choose a red ball from a bag containing 10 black balls, 5 red balls and 15 blue balls.**

If n peoples are seated around a table, in how many ways can they shake their hands, such that nobody crosses their hand.

Counting the number of expressions containing n pairs of parentheses.

There are 2 vacant positions for the president and a vice president of a club. The post can be given to any of the 50 members of the club and a member can take more than one cabinet position. In how many ways can the 2 vacant positions be filled?**50^2**

50C2

50P2

50!

A bag contains five black balls, seven white balls, and nine red balls. The number of ways in which three balls can be drawn from the bag so that all the three drawn balls will have different colors is

945

63

21**315**

What is the total number of paths from (-3,-2) to (5,6) without crossing the line passing through (-3,-2) and (5,6) (i.e., without crossing the diagonal)?

132**1430**

429

4862

Evaluate 20C4×21P2/100C99

2034900**20349**

244188

24418800

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