2 a) Six friends together with their respective partners all meet up for a meal. To commemorate the occasion, they arrange for a photograph to be taken of all 12 of them standing in a line. i) How many different arrangements are these if each friend is standing next to his or her partner? ii) How many different arrangements are there if the 6 friends all stand together and the 6 partners all stand together? b) A group of 9 people consists of 2 adults, 3 boys and 4 girls. In how many ways can a team of 4 be chosen if i) both adults are in the team? ii) the girls are either all in the team or all not in the team? iii) at least 2 boys are in the team?

Q: At a library 200 people were surveyed about magazines they read. 120 read Time, 75 read US News, 45…

A: Given : In a survey,  the total number of people were read magazines                        = 200…

Q: 3. There are 64 children in year 4. a) 8 are off sick. What fraction of children is left? b) 48 stay…

A: Two basic math word problems are given. Both are part of fractions. We have to solve these by using…

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: Of 13 students in a class,4 will be chosen to go on a felid trip.how May different ways can they be…

A: Combination of number of objects is their arrangement without considering the order while…

Q: How many ways can the letters of the word BOULEVARD be arranged in       order? b)How many ways can…

A:

Q: A class has 10 students. How many ways can the class be grouped into 2 groups of equal size.

A:

Q: There are five men and three women in a room. How many committees of 4 people can be chosen from the…

A:

Q: 4.) How many ways are there to seat 6 people in a row?

A: given data  we have to find number of ways to arrange 6 peoples in a row.

Q: 3. At graduation, 11 friends decide to take a group picture together. In how many ways can this…

A: 11 friends ,  Want to take a group picture together No. of ways = ? (Group of friends can be…

Q: Out of 420 people in a club, 40% of them are over 30 years old.Of the people under 30 years of age ,…

A: Please refer the attached image for complete solution.

Q: In a survey of 1000 students it was found that 840 own a cell phone, 450 own an MP3 player and 370…

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: A restaurant offers a menu with 3 starters, 6 main courses and 7 desserts. a) How many different…

A: (a) We assume that a 3-course meal include one starter, one main course and one dessert.      Then,…

Q: n a stock room of a car dealership, there are 4 red, 2 white, and 3 blue flags. There are three flag…

A: Given that there are a total of 9 flags with 4 red, 2 white, and 3 blue flags

Q: A small company of 30 employees needs to choose 6 people to plan out their annual holiday party Each…

A: A small company of 30 employees needs to choose 6 people to plan out their annual holiday party.

Q: A park bench can seat 3 people. How many seating arrangements are possible if 3 people out of a…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: a) In how many ways can the choreographer choose the dancers if the company has 20 dancers? 24…

A: here use combination

Q: A club has 11 members. Five are to be chosen to go as a group to a national meeting. If the club…

A: The total members in the club is 11. Of them, 7 are men and 4 are women. The main objective is to…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.