Consider 2 classes, the first with 5 students, and the second with 7 students. From this group of 12students, a pair of students (that is, an unordered set of 2 students) is to be selected. How many choices are possible if the pair of students includes one student from each class?

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: On a ballot, the candidates for each office are listed together under the office for which they are…

A: Number of candidates in one office is 5. Number of candidates in another office is 3.

Q: How many different teams of 44 can be chosen from a group of 1818 children and 1515 adults if each…

A: It is given that the number of children is 18 and the number of adults is 15.

Q: Assume that there are 11 girls and 9 boys in the neighborhood club, and a team of 6 is to be…

A: As there are 11 girls and 9 boys now if a team of 6 is to be selected. 1) Number of different teams…

Q: Assume that there are 9 girls and 8 boys in the neighborhood club, and a team of 5 is to be…

A: As there are 9 girls and 8 boys now if a team of 5 is to be selected.1) Number of different teams…

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A: From the above data We are given that Total number of cards = n =52 No of selected cards = r =3

Q: How many different teams of 4 can be chosen from a group of 16 adults and 18 children if each téam…

A: Given : 16 adults and 18 children If each téam must have at least two adults on it , then there are…

Q: How many different teams of 4 4 can be chosen from a group of 15 15 children and 17 17 adults if…

A: Given: Number of children = 15 Number of adults = 17

Q: Suppose that a candy shop sells eight different kinds of candies: 50 cherry, 50 strawberry, 40…

A: Total number of candies = 310 Number of candies to be selected = 7

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25 (b)…

A:

Q: A one-topping pizza consists of choosing a crust, a type of cheese, and one topping. If there are 4…

A:

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: In volleyball, players on the same team rotate through all positions so no particular player is…

A: The total number of players are 12. The team formed should be of 6 players. Therefore, 6 players can…

Q: Assume that the candle manufacturer has 7 types of round candles and 5 types of square candles…

A: Permutations and combinations: When one has to choose among a set of objects or people, then…

Q: At the horse races (with ten horses competing), in how many ways can the top three places be…

A: Permutation: The number of different arrangements of ‘r’ elements from a set of‘n’ elements is…

Q: Suppose we want to choose 7 objects, without replacement, from 9 distinct objects. (a) How many ways…

A:

Q: A club with nineteen members is to choose three​ officers: ​ president, vice-president, and​…

A: Permutation:   It is nothing but  an arrangement of objects with the definite order.   Let n is the…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

Q: For the new fall season, a network president has 11 shows in development, and 8 openings in the…

A: The network president has 11 shows in development . There are eight openings in the prime time…

Q: A take-out restaurant offers 6 different kinds of sushi. If they have exactly 4 pieces of eachkind…

A: Given: There are 6 different kinds of sushi, with exacctly 4 pieces of eachkind. To determine:…

Q: A credit card company gives each of its customers a 4-digit PIN where each digit is selected from…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (a) How many…

A: We can find answer to both the question as below

Q: If you can choose one item from a group of M items and a second item from a group of N items, then…

A: we have chose 1 item from a group of M items  and second item from a group of N items

Q: For a group of 9 representatives, how many committees of size 3 are possible without any…

A:

Q: A family has nine children. If this family has exactly five boys​, how many different birth and…

A: Given,A family has 9 childrens

Q: Find the number m of ways that a class X with ten students can be partitioned into four teams A1,…

A:

Q: In a certain get together, there was a basket of fruits for every three guests, a basket of cookies…

A: Let the number of fruit baskets be x, the number of cookies baskets  be y and the number of chips…

Q: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

A: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

Q: Assume that there are 8 girls and 12 boys in the neighborhood club, and a team of 6 is to be…

A: Given information: Number of girls, g = 8 Number of boys, b = 12 A team of 6 is to be selected. It…

Q: A student wants to buy 3 CDs. Assume that they are interested in 4 CDs featuring the piano, 6 CDs…

A: The total number of ways of choosing 3CD's=C313=286 If all the CD's are same that are chosen, then…

Q: A club with eighteen members is to choose three officers: president, vice-president, and…

A: topic - permutations and combinations

Q: mball machine dispenses 5 varieties of gumball (red, blue, green, yellow, and pink). How many…

A: a. The collections of 10 gumballs, at least 6 of which are red are ,  The cases obtained are  6 red…

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit…

A: Given problem Given that   In the United States, telephone numbers consist of a three-digit area…

Q: Assume that there are 10 girls and 8 boys in the neighborhood club, and a team of 8 is to be…

A:

Q: in how many ways can a hand of 5 cards be dealt such that 2 are black and 3 red cards?

A: Given:  There are 52 cards on the deck. There are 26 red and 26 black cards on the deck. Formula…

Q: 2. In a group of 6 males and 4 females, four technologists are to be selected. In how many different…

A: Since you have posted multiple questions, as per our guidelines, we have provided answer for first…

Q: (a) If a student must answer 8 of 12 questions on an examination, how many different selections of…

A: Given:  A student must answer 8 of 12 questions on an examination  To find:a) The different…

Q: f any arrangement of letters is considered a word, and there are 21 consonants and 5 vowels to…

A:

Q: From a group of 4 men and 5 women, how many committees of size 3 are possible a) With no…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: A man has eight shirts and three ties. Assuming that they all match, how many different…

A: Given that, Man has 8 shirts and 3 ties How many different combinations can he wear?

Q: How many unordered sets are there of two items chosen from eight?

A: To find unordered sets of two items chosen from eight. Number of unordered sets r chosen from n is…

Q: Suppose a library has at least 6 copies of mathematics book, at least 6 copies of a physics book,…

A:

Q: Find the number of ways of selecting exactly one of the two best applicants in a selection of two…

A: Given problem Given that

Q: How many different 4​-person teams​ (order does not​ matter) can be put together from a group of 27…

A: We have to choose 4 people from 27 persons and the order does not matter. So we will use the…

Q: Out of a population of 52 people, how many possible samples of size 2 are there?

A: Given information- Population size, n = 52 Sample size = 2 We have to find the number of possible…

Q: Suppose Fred has 2 pairs of pants (blue and black) and 3 shirts (red, blue, and black).  Which of…

A:

Q: In how many ways can a large retail store select 3 sites on which to build a new store if it has 12…

A: We have to find given combination possible.

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: From a group of 10 men and 12 women, only 5 will randomly sit down in a row of 5 chairs. How many…

A: Solution :-

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.