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: Suppose we want to choose 5 colors, without replacement, from 14 colors. a) how many ways can this…

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Q: 2. In a group of 45 students, 23 take history, 18 take biology and 10 take both history and biology.…

A: Given :  Total number of students = 45 Number of students taking history = 23 Number of students…

Q: a) Transport vehicles leaving the port with containers must have the containers tagged based on…

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Q: From a total of 9 houses, 3 were of red paint, 2 of green paint and 4 of yellow paint. Determine the…

A: The total number of families are = 9. and total number of houses are 9, where 3 have red paint, 2…

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

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Q: In a school of 100 students, 70 students play either football or cricket with 40 students that play…

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Q: 2) 100 interviewees interviewed for a position at a five star hotel. From the interviewees, 50 had a…

A: Given that, 100 interviewees interviewed for a position at a five star hotel. From the interviewees,…

Q: How many different ways can 7 students consisting of 4 boys and 3 girls sit in a row if ; a. They…

A: Represent the 7 seats in 7 blocks where each a boy or girl can be seated in each block.  Fill each…

Q: 4. There are 256 children in the juniors. a) Half have sandwiches, how many have school dinners? b)…

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Q: The Reverend minister of a church always insist that every member shake hands with every other…

A: Given Data : There are 90 members in the church To Find : Total number of handshake   In the…

Q: A mother, father, and their three children are to line up for a photo. In how many ways can these…

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Q: 5.) 5 WOMEN AND 6 MEN ARE STANDING IN A LINE. HOW MANY ARRANGEMENTS ARE POSSIBLE IF ANY INDIVIDUAL…

A: No of people = 5 women + 6 men = 11

Q: A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are blue. If…

A: Given, A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are…

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: There are 100 students who are taking history or sociology. If 10 are taking both courses and 45 are…

A: It is given that n( History or Sociology ) = n( H or S ) = 100n( only History ) = n(Only H) = 45n(…

Q: Count.... a) 18 5 b. How many different 5-person teams can be formed from 15 students?

A: a) 8568 b) 3003

Q: . evaluate perm(5,3)= b. evaluate perm(22,6)= c. evaluate comb(5,3)=

A: a. evaluate perm(5,3)=? b. evaluate perm(22,6)=? c. evaluate comb(5,3)=?

Q: A pyramid is going to be built with the following number of bricks. Three thousand eight hundred…

A: number oh bricks need for each flood decreases in arithmetic progression the sequence is…

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

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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: A group of 100 people touring Europe includes 38 people who speak spanish, 58 who speak portuguese,…

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

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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: If 5 students are to be seated in 5 chairs, how many ways can they be seated in a circle?

A: Let, n be the number(n)=5 The total number of arrangement = 1 x (n-1)!…

Q: If Joe only has room for 2 of his 6 flags on his flagpole, how many different ways can they be…

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Q: Fifteen books are to be places in a shelf. The 15 books are composed of: 6 math books, 5 science…

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Q: Of 45 members of the Campus Club, 27 had camped at Yellowstone, 23 had camped at Yosemite, and 18…

A: There are 45 members of the Campus Club, 27 have camped at Yellowstone, 23 have camped at Yosemite,…

Q: Sri and her father are piling logs at their backyard. The first layer has 15 logs, the fifth layer…

A: Given Data: Number of logs in the first layer a1=15 Number of logs in the first layer a5=7 Total…

Q: a) Every Saturday, you spent 2 and 1/5-hours biking, 6 and 12 hours sleeping and 1 and 1/3 hours…

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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.