Show your solutions) In how many ways can 6 books be arranged on a shelf if:   a.) any arrangement is possible?   b.) 3 particular books must always stand together?   c.) two particular books must not follow each other?

Q: A teacher has 4 students and 8 different candies. In how many different ways can he give all candies…

A: Given: A teacher has 4 students and 8 different candies.

Q: 1. In the KAU prize giving day, 9 women and 6 men are selected from the CS denartment

A: Given: Number of women selected =9 number of men selected =6

Q: Someone is planning a dinner party. They want to pick one bottle of wine to go with each of the four…

A: The number of courses is 4 The number of wine bottles is 8

Q: Eight members of the committee will be chosen from 15 senior and 10 junior students. 13.) If there…

A: We have given that  Senior students = 15 Junior students = 10 Total number of students = 15 We have…

Q: Suppose we want to choose 3 objects, without replacement, from the 4objects pencil, eraser, desk,…

A: We have given that we want to choose 3 objects, without replacement, from the 4objects pencil,…

Q: The subalternate of “No vegetarians eat meat” is: a. Some vegetarians are not eaters of meat b.…

A:

Q: 3. Sophia has a bowl of 15 red, 15 blue, and 15 orange pieces of candy. Without looking, Sophia…

A: (a) Sophia has to grab (3+3+3)+1 = 10 candies to make sure she has at least 4 of the same colour.…

Q: a) In how many ways can 9 people be arranged in a line if there are no restrictions? b) In how many…

A:

Q: m, John, Fred, and Bill are friends whose occupations are (in no particular order) nurse, secretary,…

A: we are asked  find the occupation for the friends

Q: 7.) Consider the smallest individual cubes and assume all stacks are solid. Determine the number of…

A: Consider the first figure, the length is 6 cubes, width is 2 cubes and height is 2 cubes. Total…

Q: 9) Oceanside Bike Rental Shop charges a 15 dollar fixed fee plus 7 dc hour for renting a bike.…

A:

Q: 1-In which condition the LCM  of two numbers is one of the numbers? Give an example? 2-In which…

A:

Q: Ax) b- a -dx = Ax)+f(a+b- x) 2

A: To prove:∫ab f(x)f(x)+f(a+b−x)dx=b−a2 Let, I=∫ab f(x)f(x)+f(a+b−x)dx    ...(1) Since, we know that…

Q: 17. The science club members are to work in pairs on an experiment. a) If there are eight members…

A:

Q: 1) Find the number of permutations of all the letters of the w following conditions

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: How many four letter words beginning and ending with a vowel without any letter repeated can be…

A: As per our guidelines we are supose to do only one questionGivenword is "MATHEMATICS"No.of letters…

Q: In a stack of cards, each card has a number and letter on opposite sides. You are told that all…

A: Each card has a number and a letter on opposite sides. Any number that is even as well as divisible…

Q: (9) Number of ways to scoop two unordered pairs from a set of 10 different elements. Assume no…

A: Let there are n distinct elements a1,a2,a3, . . . . . . . an And two set A and B, they should be…

Q: a) How many different trains can be built with a length of 10 units?

A: (a) Number of trains built with a length of 10 units is

Q: a) How many words (with or without any meaning) can be formed by arranging the letters in the word…

A:

Q: In how many ways can the letters of the word "KATHI" be arranged? Show work. A committee of 3 is to…

A: d) The word is given as “KATHI”.

Q: Let W=set of all positive integers. A={1,2,3,4,5}, B={2,4,6,8,10}, C={1,3,5,7,9}, and…

A: Given info: W=set of all positive integers. A={1,2,3,4,5}, B={2,4,6,8,10}, C={1,3,5,7,9}, and…

Q: ural numbers? 2 3

A: In how many different ways can the number 45 be written as the sum of consecutive natural number?

Q: Carefully analyze each of the following things taking into account that the points share the same…

A: c) In 1,2,3,4,5 and 6 there are 6 digits. And repetition is not allowed. So we can select the first…

Q: 1.) boys and girls are alternating 2.) 2 particular people must not sit next to each other 3.) if…

A: 5 boys and 5 girls be seated in row of 10 chairs

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.