There are many houses on Warp Drive in Kirk, Missouri. Ninety houses have cable TV. Fifty-two houses have a pool. Sixty-eight are one-story houses. There are 49 houses that have a pool and cable TV There are 43 one-story houses with pools. There are 57 one-story houses with cable TV. There are 42 one-story houses with cable TV and a pool. And there are 4 houses that are not one-story and do not have a pool or cable TV.

Q: There are two roads between towns A and B. There are three roads between towns B and C. How many…

A: There are two roads between towns A and B, and three roads between towns B and C. The number of…

Q: There are 6 men and 7 women in a ballroom dancing classes.If 4 men and 4 women are choosen and…

A:

Q: There are 15 different courses and 18 students in a school. Every student takes 4 courses. Show that…

A: Given, There are 15 different courses and 18 students in a school. Every student takes 4 courses.…

Q: There are 8 nickels, 5 dimes, 7 quarters, and 6 loonies in a piggy bank. You are thinking of…

A: Given, in a piggy bank, there are  8 nickels, 5 dimes, 7 quarters, and 6 loonies.

Q: A car manufacturer allows you to customize and order vehicles on their website. When customizing…

A: Given: There are 2 different sizes of the engine, 2 different types of transmission, 8 different…

Q: A man has 3 different pairs of shoes, 8 different pairs of socks, 4 different pairs of slacks, and 2…

A: We have given that 3 different pairs of shoes 8 different pairs of socks  4 different pairs of…

Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: The table d'hote (complete meal) at a french restaurant consists of a salad, enree, and a dessert.…

A: There are 2 salad choices, 5 entrée choices, and 3 dessert choices.

Q: The supreme choice pizza at Pete's Pizza contains 3 different types of meat and 2 different…

A: It is given that a supreme choice pizza at Pete’s Pizza contains 3 different types of meat and 2…

Q: The California license plate has one number followed by three letters followed by three numbers. How…

A: GivenCalifornia license plate has one number followed by three letters followedby three numbers…

Q: How many different committees can be formed from 7 teachers and 40 students if the committee…

A: Solution-: Given: Number of teachers =7, Number of students =40 We want to find how many different…

Q: The organizer of a conference is selecting workshops to include. She will select from 9 workshops…

A: Here we have to use concept of combinations.

Q: How many different committees can be formed from 12 teachers and 39 students if the committee…

A: No. of teachers=12no. of students=39committee should consist of 3 teaches and 2 students

Q: You and 3 friends are moving into a new apartment-style dorm. The dorm has 3 bedrooms, one with two…

A: There are totally 4 members. These 4 members must be arranged in 3 bed rooms. One bedroom has two…

Q: There are 6 boys playing soccer. 3 boys go home. Then 1 more boy goes home. How many boys are there…

A: Given that there are 6 boys playing soccer, 3 boys go home then 1 more boy goes home. We have to…

Q: A Convener and a Secretary are to be chosen from group of people consisting of 50 people. Explain…

A: i) We can select A as Convener in only 1 way. We can select Secretary from (50-1)=49 people in 49…

Q: There are 15 children in soccer training squad. A team consist of 11 players. If two children can…

A: Given: 15 children To find: Solution

Q: Each marble bag sold by Deshaun's Marble Company contains 5 orange marbles for every 6 green…

A:

Q: A southeast regional salesman has eight destinations that he must travel to this month:Atlanta,…

A: Given salesman has 8 destinations. Therefore different possible routes are 8! ways = 40320 ways.

Q: A designer has designed different tops, pants, and jackets to create outfits. How many different…

A: Given six tops, five pants, two jackets

Q: A state has license plates that consist of 2 letters followed by 3 numbers and each letter and…

A:

Q: a card store received a shipment of 12 cartoons of sports cards . Each cartoon contains 20…

A:

Q: Radio stations that are on the eastside of a nation have call letters consisting of a W followed by…

A: Here we have to number of five letter call letters starting from W

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

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

Q: Motors Inc. manufactured 306 cars with automatic transmissions, 237 with power steering, and 62 with…

A:

Q: There are 4 roads leading from Bluffton to​ Hardeeville, 9 roads leading from Hardeeville to​…

A: Given the number of roads leading from Bluffton to Hardeeville=4 The number of roads leading from…

Q: A bag contains three red marbles, one green one, one lavender one, three yellows, and three orange…

A: Total number of marbles, n = 3 red + 1 green + 1 lavender + 3 yellow + 3 orange = 11 Number of red…

Q: A married couple decides to have a party. The husband has 8 friends and the wife has 9 friends.…

A: Solution: Given information: Husband has 8 friends  Wife has 9 friends  Total friends = 8+9= 17

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.