A class has 17 ​students, of which 3 are seniors. How many committees of size 3 can be selected if at least one member of each committee must be a​ senior? The number of committees is nothing.

Q: A committee has 20 people.  In how many ways can a President, Vice-President, and Secretary be…

A: Note:  Permutation: We kno that, nPr represents the selection an ordered set of ‘r’ objects from a…

Q: How many six-person volleyball teams be made from a group of six men and three women if: a. If two…

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

A: According to provided data, there is total of 15 children (C) and 17 adults (A). Therefore, the…

Q: there are 11 members on a board of directors. if they must form a subcommittee of 6 members, how…

A: we use the formula nCr = n!/(n-r)! * r!

Q: n consists of 10 albums, each containing 42 pages. How many stamps are in the total collection if 40…

A: Introduction: Different symbols are used in mathematics. One of the most common math symbols is the…

Q: How many 4-digit combinations can be made from the digits 0-9?

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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: 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: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

Q: a) How many three-digit numbers less than 700 can be made using the digits 9, 7, 4, and 2? (Each…

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

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Q: In a club with 7 male and 11 female​ members, how many 4-member committees can be chosen that have…

A: (a) From the given information, the club with 7 male and 11 female members. And 4-member committee…

Q: How many ordered lists are there of seven items chosen from twelve?

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Q: How many ordered lists are there of two items chosen from twelve?

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Q: A club has 35 members, 8 of whom are Civil Engineers. In how many ways can a committee of 4 be…

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Q: there are 11 members on a board of directors. if they must form a subcommittee of 6 members, how…

A: we use the probability for selections formula, nCr = n!/(n-r)! * r!

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: Of 18 possible​ books, you plan to take 6 with you on vacation. How many different collections of 6…

A: Given, Total  number of books = 18

Q: How many committees are possible if the committee must have a least two men?

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: Assume that a grade of A,B,C,D, or F is assigned to each of 9 students. In how many ways can grades…

A: From the provided information, The grades are A, B, C, D or F Total students = 9

Q: How many three-digit numbers can be formed from the digits 1, 2, 3, 5, and 6, if each digit can be…

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Q: The Student Council at a certain school has 11 members. Out of those members, a committee consisting…

A: Given information: The student council at a certain school has 11 members. From the 11 members, a…

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

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Q: A four-person committee is to be selected from an organization’s membership of 12 people.  How many…

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Q: A teacher has 24 colored pencils and 18 pictures to be placed in groups with the same number of…

A: Question 3:             It is given that a teacher has 24 colored pencils and 18 pictures. The…

Q: A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each). How…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: A company buys 9 computers, and it plans to connect each pair of computers by a cable (one cable per…

A: Given that there are total 9 computers. They will connect each pair of computers. That means we have…

Q: how many ordered lists are there of three items chosen from six ?

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Q: How many different teams of 4 members can be selected from a pool of 20 applicants?

A: The combination formula is given by

Q: How many ordered lists are there of two items chosen from five?

A: To find the number of ordered lists.

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 words, with or without meaning, each of 3 vowels and 3 consonants can be formed from the…

A: Permutation is an arrangement or order of selecting some of the elements from a group or a set of…

Q: In a certain state, all car license plates have four capital letters followed by three digits. How…

A: Given Car license plates have 4 (A to Z) capital letters followed by 3 (0 to 9) digits

Q: A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?

A: We can find the answer as below.

Q: How many different selections of three books can be made from a set of fifteen books?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…

Q: A photographer is asked to submit seven photographs from a collection of 14 for an exhibit. In how…

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Q: law enforcement officers if each committee consists of 6 law enforcement o

A: Given: n = 9 r= 6

Q: In a certain company 80 of the employees are men. What is the total number of employees if 5 out of…

A: given In a certain company 80 of the employees are men. To Determine the total number of employees…

Q: From a club of 16​people, in how many ways can a group of six members be selected to attend a​…

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Q: In a round-robin tennis tournament, every player meets every other player exactly once. How many…

A: let x = number of players Each player plays x-1 matches BUT a vs b is the same as b vs a So 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: A club with 23 members is to select a committee of six persons. In how many ways can this be done?

A: Given: The number of members in a club is equal to 23, To find: The number of ways of selecting a…

Q: A drawer contains 20 pens, of which 4 are red, 7 are black, and 9 are blue. At the least, how many…

A: Given Data: Number of red pens=4 Number of black pens=7 Number of blue pens=9   Total number of…

Q: How many license plates are possible if they consist of 1 digit followed by 1 letter followed by 5…

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Q: How many license plates are possible consisting of 4 letters followed by 3 digits if the first…

A: The license plate consists of 4 letters followed by 3 digits. Thus, it has 7 places to fill up.…

Q: From a group of 10 physicians, in how many ways can four people be selected to attend a conference…

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Q: A five-person committee is to be selected from an organization's membership of 19 people. How many…

A: It is given that, An organization has 19 people out of which 5 person committee is to be selected.…

Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels if order is…

A: There are 5 vowels and 21 consonants. Here, the order is important.

Q: If there were to be 15 boys and 13 girls at a party and the host wanted each to be given exactly…

A: