By hand please. show step-by-step: A group of four students is to be chosen from a 35-member class to represent the class on the student council. How many ways can this be done?

Q: A group of 10 friends go to a movie theater to see a newly released film. The friends consist of…

A: As per the given information 5 married couples are there and each couple must sit together Possible…

Q: if there are no restrictions? if Holly and Sam cannot sit together?

A: here given ,  Holly, Parker, Jace, Ola, Amir and Sam have gone out to a football game together, They…

Q: How many ways can you choose first, second, and third place winners from 15 people?

A: The first place winner can be chosen as 15 ways. The second place winner can be chosen as 14 ways…

Q: Orders for the Valentine’s Day bouquets. Each student could choose any combination of red, pink,…

A: Given,no.of different combinations=4  (red , pink , white , yellow)

Q: how many student have seen none of these movies and how many have seen 2 or more?

A: Given that 18 had seen The Matrix(M)24 had seen Star Wars (SW)20 had seen Lord of the Rings (LotR)10…

Q: Sandra is writing an article and taking pictures for the school newspaper. She chooses three…

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Q: Choose the letter of the correct answer. A certain elementary school club has 50 members, 20 of…

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Q: Twelve people are on a committee. If five of them are to be chosen to serve on a subcommittee, how…

A: There are total 12 people.  Since it is a group of people so order does not matter. So we will use…

Q: Committee: The Student Council at a certain school has seven members. Four members will form an…

A: Given,Total no.of members=7

Q: A child has 20 pieces of Halloween candy. They are as follows: 6 of them are chocolate bars, 9 are…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! Selecting…

Q: For the student's college council committee, in how many ways can you select a committee of 3…

A: As given That student council committee , The order of selected committee students is not needed…

Q: Mr. H has a collection of 500 vessels. In how many ways can he name his favorite and second favorite…

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Q: At a ballroom dance lesson, the instructor chooses 3 men and 3 women to demonstrate a new pattern.…

A: There are 9 women and 7 men in the class, the instructor chooses 3 men and 3 women to demonstrate a…

Q: A class consists of 12 students ​(six boys and six ​girls) and one teacher. In how many ways can the…

A: Here there is a class consists of 12 students where there is 6 boys and 6 girls and 1 teacher We…

Q: There are 30 people in the class. We need to select 5 people to form a the committee, how many…

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Q: 8 people stand in line at a movie theater. Into how many different orders can they be arranged? 40…

A: 1. Number of people standing in a line = 8 If the people are arranged in a line at a movie theater,…

Q: Books: Josephine has seven chemistry books, three history books, and four statistics books. She…

A: number of ways to choose r objects from n different objects  =ncr =n!/[(n-r)!r!]

Q: Select a committee of seven members from a group of six women and eight men. The order of selection…

A: Given that  A committee of seven members  Group of 6 women and 8 men

Q: How many ways can 4 people sit in a row of 7 chairs? The number of ways 4 people can sit in a row of…

A: Given: number of chair (n)=7 number of people (x)=4

Q: Renae, Nexael, Braden, Lovely, and Vanessa are attending a play and want to sit together in a row.…

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Q: student organization of 40 wants needs three people to cover ticket sales at an event. How many…

A: Given n=40 x=3

Q: Your class of 15 students has assigned a group project. You must break up into three groups of five…

A: Formula:   If there are n objects. If there are k1 of type 1, k2 of type 2 and so on km of type m…

Q: Four math clubs go to a conference and meet up for lunch. They introduce themselves to each other…

A: The scenario in which four math clubs go to a conference and meet up for lunch.Every member of each…

Q: Ten students are chosen to compete for seven scholarships: one is for $5,000, two is for $3,500…

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Q: There are 20 members of the debate team, including 9 girls and 11 boys. Complete parts (a) through…

A: Given 20 members=9 girls and 11 boys  r!=r(r-1)(r-2)x...x3x2x1

Q: igh school classes will be chosen to participate in a school activities survey. There are 21 high…

A: Given:6 high school classes will be chosen to participate in a school activities survey.There are 21…

Q: The jar of change contains: pennies,  nickels,  dimes, and  quarters. If you grab five coins from…

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Q: In an art class with 15 boys and 14 girls, five girls and four boys will be chosen to sing a special…

A: Given: Number of boys=15Number of girls=14 The number of ways five girls and four boys will be…

Q: In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the…

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Q: A group of 9 women and 6 men must select a 4-person committee. How many committees are possible if…

A: The group contains 9 women and 6 men. A 4-person committee is selected. a) The number of ways to…

Q: Twelve people need to be photographed, but there are only five chairs. (the rest of the people will…

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Q: We want to select 3 customers form a group of 8 customers to give each one a gift. How many possible…

A: Combination:   It is nothing but the selection of objects where the order of selection is not…

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)!