Discrete Mathematics | Week 1

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

c. 20160

2. 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?

c. 210

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

d. 6!/2!×7!/(2!×2!)

4. 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?

c. 123480

5. What is the coefficient of the 6^th term in the expression ( 5x⁴/13 − x³ /2 )⁷

b. -525/5408

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

b. 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.

7. 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?

a. 50²

8. 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

d. 315

9. 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)?

d. 4862

10. Evaluate (²⁰C₄ײ¹P₂) / ¹⁰⁰C₉₉

b.  20349