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

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

A:

Q: A class has 28 students. In how many different way can four student form a group for an…

A: GivenTotal no.of students in a class(n)=28No.of students form a group for an activity(k)=4

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

A: Follow the steps.

Q: in how many ways can 5 children be arranged in a line for a photograph?

A:

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

A:

Q: A restaurant offers 20 appetizers and 40 main courses. In how many ways can a person order a…

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

Q: How many combinations can the seven colors of the rainbow be arranged into groups of three colors…

A:

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: How many ways can 12 students standing in a line be arranged if John must be first in line?

A:

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: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: A photographer is asked to submit 7 photos from a collection of 14. How many ways can the photos be…

A:

Q: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10. a. How many…

A: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10.   a. Number of…

Q: With 20 people seated around a tabke, how many ways can 3 people be selected without any being…

A: It is given that there are 20 people seated around a table. The total number of ways of selecting 3…

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: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are blue. If…

A: Given, A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are…

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 arrangements can 7 women and 7 men be placed in a line if all the women line up first?…

A:

Q: Consider a Little League team that has 15 players on its roster. How many ways are there to select 9…

A:

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: A camp counselor and six campers are to be seated along a picnic bench. In how many ways can this be…

A:

Q: From a group of 20 children, how many must you choose, if you want to make sure two of them have…

A: There are 12 month in a year, thus let m=12. Let n denote the number of chosen children who have…

Q: In how many ways can a president, secretary and treasurer be selected from a group of 15 people?

A: we know that one person cannot hold more than one post (president, secretary and treasurer) then we…

Q: In how many ways can a group of 6 students be selected from 7 students?

A:

Q: In how many different ways can 9 people arrange themselves in a line to receive service from a…

A: Given information: There are total 9 people arrange themselves in a line to receive service from a…

Q: Suppose you have a set of cups and saucers which are red, orange, green, light blue, dark blue, and…

A: Number of different coloured coffee cup=6 Number of different coloured saucer=6

Q: In how many ways can three taxi drivers be assigned to nine cars?

A: The number of taxi drivers is 3 and the number of cars is 9.

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

A:

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

A: To find the number of ordered lists.

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: How many ways can 7 people fall in line if 2 persons doesn’t want to be seated next to each other?

A:

Q: In how many ways can six pictures be selected from a group of ten different pictures?

A: It is given that 6 different pictures are to be selected from a group of 10 pictures, therefore,

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: 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: 2. How many 4 letter arrangements can be made from the letters MILKE D?

A: Explained below

Q: you have 11 tubs of paint how many distinct color groupings can you make with your paint?

A: Total given colors are   11 Total distinct colors grouping   ?   we can solve this question with the…

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: If a club consists of 13 ​members, how many different arrangements of​ president, vice-president,…

A:

Q: If there are 13 employees in a club, in how many ways can they choose a dishwasher and a bouncer?

A: Given information- We have given that there are 13 employees in a club. They want to choose a…

Q: A boy has 2 red, 3 yellow and 3 green marbles. In how many ways can the boy arrange the marbles in a…

A: We have to ans question 1 and 2

Q: How many poles will there be in a stack of telephone poles if there are 58 in the first layer, 57 in…

A:

Q: How many ways can captain, co captain and team manager be assigned to a group of 10 runners at a…

A:

Q: Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk,…

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: If a club consists of 15 ​members, how many different arrangements of​ president, vice-president,…

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

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.