A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are blue. If the child puts the blocks in a line, how many arrangements of the same color are possible?

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

A:

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: Suppose you are to arrange 9 people on a line. If 5 specific people require to be following each…

A: Given,total no.of people=9

Q: Of the eighth graders at the Paxton School, 15 played basketball, 9 played volleyball, 10 played…

A:

Q: A survey of 145 computer science students reveals that 80 own desktop computers, 95 own laptops, 30…

A: Assume number of students who has  desktop = d number of students who has laptops= l number of…

Q: (i) Determine how many rows are in the corner section of a stadium containing 3920 seats if the…

A: the total number of seats in the stadium are 3920  the first row has 10 seats,  The second row has…

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: At a blood drive, 6 donors with type O+ blood, 5 donors with type A+ blood, and 3 donors with type…

A: Given that, 6 donors with O positive blood 5 donors with A positive blood 3 donors with B positive…

Q: Of the eighth graders at Praxton School, 15 played basketball, 9 played volleyball, 10 played…

A:

Q: A boy has 4 red , 4 yellow and 5 green marbles. In how many ways can the boy arrange the marbles in…

A: Given 4 red, 4 yellow and 5 green marbles

Q: n a group of 37 children, 28 had a dog, 21 had a cat, and 17 had both a dog and a cat. How many…

A:

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

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

A:

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: A jar contains four white balls, eight black balls, and six red balls. In how many ways can two…

A: Given :Total number of balls in a Total number of white balls = 4 Total number of black balls = 8…

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: How many different signals can be made from 7 flags hung in a vertical line, using 2 identical white…

A: We have to find correct different signals can be made from 7 flags hung in a vertical line.... Here…

Q: Consider a bag containing six red marbles, two green ones, one transparent one, four yellow ones,…

A: We have 6 Red marbles2 Green marbles1 transparent marble4 yellow marbles2 orange marblesTotal no of…

Q: A shipment of 9 television sets includes three that are defective. In how many ways can a hotel…

A:

Q: In how many ways can 3 student, 4 teachers and 4 workers sit in a line if the teachers always set…

A:

Q: A family has nine children. If this family has exactly five boys​, how many different birth and…

A: Given,A family has 9 childrens

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: If six black, five red, four white, and two green disks are to be arranged in a row, what is the…

A: Permutation: the permutation is determining the number of possible arrangements in a set when the…

Q: A basketball squad consists of twelve players. (a) Disregarding positions, in how many ways can a…

A: To find the number of ways of different team possible.

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: Combination:   A combination is a selection of objects where order is not important.   If n is…

Q: In a survey of 260 students, it is found that 78 like broccoli, 103 like cauliflower, and 56 like…

A: We will solve it by Venn diagram Let A be the set who like broccoli and B be the set who like…

Q: A sock drawer contains 3 black socks, 4 blue socks, and 7 brown socks. If you pick socks from the…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: At a blood drive, 6 donors with type O+ blood, 5 donors with type A+ blood, and 3 donors with type B…

A: Given that, 6 donors with O positive blood 5 donors with A positive blood 3 donors with B positive…

Q: From a group of 28 students, how many ways can all 28 of them stand in a line [ Choose ] three of…

A: Using Permutation and Combination we can solve these questions

Q: Suppose a designer has a palette of 16 colors to work with, and wants to design a flag with 2…

A: Recall:  nCr=n!r! (n-r)! We have, n=16, r=2

Q: How many people used two modes of transportation if 1978 took public transit, 1494 drove, 818…

A: Given Information: People who took public transit = 1978 People who drove = 1494  People who cycled…

Q: From a group of 10 men and 5 women, how many committees of size 5 are possible? a.) With no…

A: Given From a group of 10 men and 5 women, how many committees of size 5 are

Q: an automobile that was tested for production defects, but assume that the number of production…

A:

Q: Suppose a designer has a palette of 15 colors to work with, and wants to design a flag with 5…

A: Given that a designer has a palette of 15 colors and he wants to design a flag with stripes, all of…

Q: A company needs to create three new departments and there are seven managers competing to run these…

A: Determine the number of ways in which can three new leaders be appointed. The number of ways in…

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 shipment of 14 television sets includes three that are defective. In how many ways can a hotel…

A: As per our guidelines we suppose to do only one question1.GivenNo.of television =14No.of defective…

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: The manufacturer plans to make scarves with 8 colored stripes. There are 16 colors to choose from…

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: 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: Assume a boat sends signals by arranging six colored flags on a vertical flagpole. If there are two…

A: There are six colored flags on a vertical flagpole out of which two are red and four are green.

Q: Consider a bag containing six red marbles, two green ones, one transparent one, seven yellow ones,…

A: Use combination theorem:

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: Consider a bag containing seven red marbles, two green ones, one transparent one, seven yellow ones,…

A: Determine the number of sets of five marbles include at most one of the red ones but no yellow ones.…

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.