Suppose a family has four children. Find the number of arrangements of exactly two boys.

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: How many possible meals are there?

A: here use fundamental of counting principle   The school canteen offers the following choices for…

Q: Five couples want to have their pictures taken. In how many ways can they arrange themselves in a…

A: Here we have to find the total numbers of ways so that they can arrange themselves in a row of…

Q: The eleven players of the CHS sepak takraw team are to be photographed for the team's tarpaulin. In…

A: Here, the question is in how many ways can 11 players can be arranged in a row.

Q: During a birthday party, how many ways can five guests, both parents, and the birthday celebrant be…

A: Follow the steps.

Q: A bride is choosing a dress for her bridesmaids. If there are 2 styles, 5 colors, and 3 fabrics, in…

A: Given that  A bride is choosing a dress for her bridesmaids. Number of styles = 2 Number of colors =…

Q: In how many ways can a boy arrange his 5 different toys in a row?

A: Given that : To find In how many ways can a boy arrange his 5 different toys in a row?

Q: If order of items is important when selecting some of n unique items, the number of arrangements are…

A: By order being important, we mean that (a, b) and (b, a) are not equal. For example, if we are…

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: In how many ways can you arrange five books along a shelf, assuming that the order of the books…

A: Given  arrange five books

Q: A car can comfortably hold a family of five. If two people among the five can drive, how many…

A: To find: The number of different seating arrangements. Given: The total number of family member in a…

Q: A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the…

A:

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different…

A: Let, N be the number of different available plansFirst operation (choice of home design) can be…

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: In how many ways can eight children posing for a photograph line up in a row?

A: 8! = 40320 ways can eight children posing for a photograph line up in a row

Q: There are 12 people at a party. If they all shake hands, how many different hand-shakes are there?…

A:

Q: There are 50 students in a class and three of them will be in a student government, either as…

A: Total number of students = 50

Q: In a group of dogs and their owners, there are exactly 20 heads and 64 legs.  How many dogs are in…

A: Let, x be No of men. y be no of dogs   Men consists of 2 legs and dog has 4 legs.   x+y=20 2x+4y=64

Q: . In how many arrangements can 7 women and 7 men be placed in a line if all the women line up first?…

A:

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 4 colors, and 5 fabrics, in…

A: Given that, Number of styles = 3 Number of colors = 4 Number of fabrics = 5

Q: A person has 8 friends, of whom 5 will be invited to a party.How many choices are there if 2 of the…

A: Combination Rule:The arrangement of r objects from n different objects is given by:

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: In how many ways can 6 bicycles be parked in a row?

A:

Q: In how many ways can Janice arrange 6 potted plants in a row?

A: Number of plants = 6

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 5 colors, and 4 fabrics, in…

A: Given: Styles = 3 Colors = 5 Fabrics = 4 The number of ways that she can select the bridesmaids…

Q: How many arrangements are possible if all the letter E must be next to each other of the word…

A:

Q: A boyscout troop has 10 members. a. How many ways can the Troup Leader select 3 members to lead a…

A: Given A boy scout troop has 10 members. To find a. How many ways can the Troup Leader select 3…

Q: Three members of an organization volunteered to serve as President, Treasurer and Secretary. In how…

A:

Q: How many different arrangements can be made using all the letters in CALGARY, if the first letter…

A: CALGARY If the first letter must be G.  Then, Starting with G, need to arrange the remaining 6…

Q: Consider a group of N people. If everyone shakes hands with everyone else, how many handshakes take…

A: The number of people in a group is N.

Q: Suppose the group of twelve consists of five men and seven women. a) How many five-person teams can…

A: A group consist of fire men and sexes women. We have to make a fire person team with 3men and 2…

Q: A class contains 8 boys and 4 girls. In how many ways can the teacher choose a committee of 4?

A:

Q: Suppose there are 20 students in our class and we want to choose 3 to sit in the front row. How many…

A: Given information There are 20 students We want to choose 3 to sit in the front row Total number of…

Q: The Schmidts are considering the purchase of 3 paintings for their home. Their decorator advises…

A: Given information- We have given The Schmidts are considering the purchase of 3 paintings for their…

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: The number of ways of choosing ten students from a class of twenty-five is the same as the number of…

A: So in this we have to find the both then evaluate to see both are same so for this I'm providing…

Q: \item How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his…

A: Note: As per our Honor code policy, we are authorized to answer only three sub parts at a time. So,…

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: If 5 horses are in a race and they all finish with no ties, in how many ways can the horses finish…

A: Given information- We have given that 5 horses are in a race. They all finish the race with no ties.…

Q: A class of 40 students is to choose a set of classroom officers composed of the President,…

A: Permutation formula : nPr = n! /(n-r)!

Q: how many hands of 33 cards can be made, where all cards are of the same suit?

A:

Q: Your club would like to form a committee that has 2 sophomores, 3 juniors, and 4 seniors. If there…

A: In this question out of 7 sophomores we have to choose 2, Out of 8 juniors, we have to choose 3 and…

Q: A class contains 8 boys and 4 girls. In how many ways can the teacher choose a committee of 5?

A: Given information- We have given that a class contains 8 boys and 4 girls. The teacher has to make a…

Q: If Kristine were to pull a marble from the jar below randomly, replace and pull another marble 75…

A: There are 15 marbles in the jar labelled 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. 1 Marble is drawn with…

Q: Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: If a family has seven children, in how many ways could the parents have three boys and four girls?

A: Since there are 7 children. To find the number of ways such that parents have three boys and four…

Q: A family has 6 kids. In how many ways could the parents have the three boys and three girls?

A:

Q: If 5 cards were picked at random from a deck of 52 cards, find P(Exactly 2 are hearts)?

A:

Q: With a group pf five men and five women, how many ways can they be arranged in a row if men and…

A: Given that  Number of women = 5 Number of men = 5