We want to form two groups of 7 out of 14 students. In how many different ways can this be done?

Q: How many different committees are possible that consist of 5 women and 3 men selected from a group…

A: For a committee, arrangement does not matter so use the combination method.  We can select 5 women…

Q: How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25…

A: The number of ways r items can be selected out of n different items is equal to C(n, r) . The…

Q: How many ways can a delegation of 4 Republicans, 3 Democrats, and 3 Independents be selected from a…

A: Given data Number of Republicans = 9 Number of Democrats = 9 Number of Independent = 4

Q: A team of 7 players is to be selected from a group of 13 people. In how many ways can this be done?

A: Given data  A team of 7 players is to be selected from group of 13 people No of ways can be this…

Q: From a club of 25 people, in how many ways can a group of six members be selected to attend a​…

A: In how many ways a group of six members can be selected from a club of 25 people.

Q: How many ways can you choose 3 distinct groups of 3 students from total 9 students?

A:

Q: In how many different ways can the director of a research laboratory choose two chemical engineers…

A:

Q: We want to form two groups of 10 out of 20 students. In how many different ways can this be done?

A: We apply combination formula to calculate

Q: In how many ways can a class of 32 students select four people to serve on a committee?

A: Total number of students in the class (n) = 32 Number of students to be selected to serve on a…

Q: A committee of 6 people, with two of the six to be designated chair and vice-chair, is to be…

A: Given : Total number of people = 20 Number of committee member = 6

Q: The football team consists of 15 members. In how many ways can a playing team of 11 players be…

A: = 1365Hence, there are 1365 ways to form a football team with 11 players from 15 players.

Q: How many ways can you select a committee of 4 student our of 10 students?

A: As per our guidelines we are suppose to answer only one question4)Given Total no.of…

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

A:

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

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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 committee of 5 students is to be selected from 16 students in a fraternity. a. In how many ways…

A: Given that a committee of 5 students is to be selected from 16 students in a fraternity. a We have…

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

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

Q: How many ways are there to choose 3 applicants from 8 job-seekers for high-paying positions in an…

A: Given information- We have given that in an engineering company 3 positions are there and 8…

Q: at a school assembly,4 out of the first 10 students were wearing spirit wear. Based on this…

A: Total number of student at school assembly = 500

Q: Your school principal wants to select a group of six students from your class of 15 students to…

A: Combination: A combination is a selection of items from a group of items, where the order of…

Q: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A:

Q: How many different ways can a group of 5 students line up to get ice cream?

A: This is type of permutation question, because here the order of placing the people in the place…

Q: A committee of size 6 is being formed from a group of 10 Republicans, 8 Democrats and 4…

A:

Q: How many ways can a teacher choose 3 out of 8 students for a field trip?

A: Need to find the number of ways a teacher choose 3 out of 8 students for a field trip.Choosing r…

Q: A committee of 6 people, with three of the six to be designated chair, vice-chair, and secretary, is…

A: 5. In a group there are 15 people. A committee of 6 people has to be selected, in which 3 must be…

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: Ten people split up into five groups of two each.  In how many ways can this be done?

A: The number of combinations of r items from a group of n items where the order is not important is…

Q: 39. How many groups can be formed from  8 students taking at least 2 at a time?

A:

Q: In a class of 18 girls and 15 boys, in how many ways can a girl get the highest grade, a boy second,…

A: Consider the given information.The number of the boys is 15 and the number of the girls is 18 girls.

Q: Before a trial, a jury had to be selected from a group of 12 males and 13 females. a. In how many…

A:

Q: From a group of 20 nurses, 4 are to be selected to work a night shift. In how many ways can this be…

A:

Q: How many ways to choose 4 out of the 10 candidates to be sent to a conference?

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

Q: In how many ways can a committee of three consisting of two lady engineers and one mal engineer can…

A: Given that  Committee consists of members  = 3  [ Lady engineers = 2 ; Male engineer =1 ] Lady…

Q: In how many ways can a committee of three men and four women be formed from a group of 10 men and 10…

A:

Q: How many ways can a group of n people be arranged in a circle that contains k equally distributed…

A: Number of ways of selecting k people from n people = Ckn = n!k!*(n-k)!

Q: How many ways can you select 3 students from a class of 30 students to serve as representatives for…

A: Follow the procedure given below.

Q: In a class of 15 boys and 10 girls, in how many ways may a committee made up of 3 boys and 2 girls…

A: Given:  15 boys and 10 girls.

Q: In a group of 6 boys and 4 girls, 4 children are to be selected. In how many ways can they be…

A: The number of ways in which r different items can be selected from n different items, can be given…

Q: In how many ways can 5 people arrange themselves in a row for picture taking?

A: Given that there are 5 people in a group.

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

Q: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

Q: A psychology lab doing research in dreams has 4 rooms (1,2,3, and 4), each containing 2 beds (A and…

A: Given: There are 3 rooms with 2 beds each. 3 pairs of twins are to be assigned to these 6 beds so…

Q: In how many ways can a committee of three men and four women be formed from a group of 12 men and 12…

A: given: Number of men = 12 Number of women = 12 The number of ways of choosing "r" from "n" is…

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: How many ways can 10 people line up if Joey and Sally cannot be next to each other? If the same…

A: here we have to use permutation ( arrangement )  Number of way r object can be arranged by taking…

Q: In how many ways can a committee of three men and four women be formed from a group of eleven men…

A: Given,no.of mens=11no.of womens=10

Q: From a group of 10 boys and 6 girls a committee of 3 boys and 2 girls is to be selected. In how many…

A:

Q: In how many ways can a committee of 4 men and 5 women be formed from a group of 12 men and 8 ​women?

A: nCr=n!r!(n-r)!

Q: How many ways can a committee of 4 be selected from a club with 10 members?

A: No of ways to select a committee of 4 from 10 members is =? We can select in 10C4 ways.   nCr= n! /…

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