You are tasked to arrange five different Mathematics books, four different Science books,and three different English books on a shelf.In how many ways can you arrange the books on the shelf such that books of the samesubject are together?O (5! 4! 3!) (3)O 5! + 4! + 3!O 5! 4! 3!O (5! 4! 3!) (3!)

Given,no.of mathematics books=5no.of science books=4no.of English books=3

Answered: You are tasked to arrange five…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 16.) A group of 2 professors and 5 students (3 grad students and 2 undergrads) go to a movie together. The professors want to sit together, and the grad students want to sit together. How many ways are there to seat this group in a row of 7 seats?
Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?
You have one pile of 11 building blocks, each one a different color, and you also have another pile of 7 blocks, again each one a different color. How many ways are there to build a tower 4 blocks high from the first pile and another tower 3 blocks high from the second pile? Assume that the colors at each level of a tower matter. (A) 318 (B) C(11,4) C(7, 3) (C) P(11,4) P(7,3) (D) P(18,7) (E) 311 (F) C(18,7) (G) P(11,4)+ P(7,3) (H) C(11,4)+ C(7,3) O A OB OC O E O F OG H.
Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways can the 10 statistics texts be arranged on the top shelf?(b) How many ways can the 8 calculus texts be arranged on the bottom shelf?(c) How many ways can the 18 texts be arranged together on a single shelf, with the statistics texts grouped together and the calculus texts grouped together?
Assume that the committee consists of 14 members including Julie. The same three offices are to be filled. (1) In how many different ways can the offices be filled if each person can hold at most one office? (2) In how many of these ways is Julie the chairperson? (3) In how many of these ways is Julie an officer?
We have 3 Physics books, 4 Math books, and 5 Chemistrybooks. The 12 books are distinct. We want to arrange them all on abookshelf. Observe that without any restrictions there are 12! ways to arrangethem on a bookshelf. Explain each answer. In how many ways can we do this(a) if the arrangement must start with a Physics book and must end with aChemistry book?(b) if the arrangement cannot end with a chemistry book?(c) if the arrangement must begin with all the Physics books?(d) if the two specific books X and Y (of the 12 books) cannot be next toeach other?(e) if all the books belonging to a subject must stay together (i.e. stay nextto each other)? (hint: The subjects themselves have to be in someorder.)
d. [Permutation] Solve the following problems - Find the number of words that can be formed by using the letters of the word "DEMOCRACY" where first letter will be always C and last letter will be R. e. [Combination] A group of 15 students is to be formed from 44 students of MATI00 Course. Among the students of the course there is 2 renowned batsmen, 3 spinners, 2 fast blowlers and 2 wicketkeepers. How many different ways this can be done so as always to (i) include 1 renowned batsman, 1 fast bowler, 1 spinner and 1 wicketkeeper; and (ii) exclude spinners? 2.
Twelve officers of an organization are to be divided into committees. In how many ways can the officers be divided into three committees composed of six, four, and two members, respectively? O 12 C6 +12 C4 +12 C2 O 12 C6 *12 C4 *12 C2 O (12)(4)(2) 12 6 4 2,
In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together? 14! 10! x 4! 13! - (10! x 4!) 13! x 4!
In how many ways can 10 engineers and 4 doctors be seated at a round table if no two doctors sit together? * 9! x 10P4 10! x 10P4 10! x 4! O 13!
A quiz contains 10 questions. There are four possible answers for each question.(a) In how many ways can a student answer the questions on the test if the student answersevery question? (b) In how many ways can a student answer the questions on the test if the student canleave answers blank?

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