A grocery store sells 10 different types of sodas sold in six-packs with at least 200 of each type in the store. In a hurry you grab 20 six-packs from the refrigerator without paying attention to the type. How many different combinations of 20 six-packs can be purchased?

Q: At a furniture store, there a 4 different sizes of sofas, 7 different colors of fabric , and 8…

A: Given that, No.of  different sizes of sofas = 4 No.of different colors of fabric =7 No.of different…

Q: There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a…

A:

Q: In a cohort of 46 graduating students, there are 5 different prizes to be awarded. If no student can…

A: A Permutation is the choice of r things from a set of n things without replacement and where the…

Q: How many license plates consisting of three letters followed by three digits contain no letter or…

A: Here we have to find  out the combination of licence plate where repetition  of  letters and digits…

Q: A car dealership offers 10 different upgrades with each of the vehicles it sells. If a customer can…

A: Given data; A car dealership offers 10 different upgrades with each of the vehicles it sells.  To…

Q: How many ways can 2 students be selected from a group of 5 students if order matters?

A: Solution-: We find number of ways 2 students be selected from a group of 5 students if order…

Q: There are 8 nickels, 5 dimes, 7 quarters, and 6 loonies in a piggy bank. You are thinking of…

A: Given, in a piggy bank, there are  8 nickels, 5 dimes, 7 quarters, and 6 loonies.

Q: There are nine different marbles in a bag. A student reaches in and randomly draws one marble at a…

A: Given there are nine different marbles in a bag. A student reaches in and randomly draws one marble…

Q: Motors Inc. manufactured 325 cars with automatic transmissions, 216 with power steering, and 89with…

A: We have given,

Q: A friend of mine is giving a dinner party. His current wine supply includes 11 bottles of zinfandel,…

A:

Q: A dog shelter is giving away 16 different dogs, but you have room for only 4 of them.  How many…

A: Given, Number of different dogs given by shelter =16 There is exactly 1 room that can accommodates…

Q: A manufacturer knows from experience that for every 100 widgets that are produced at her factory, 3…

A: Given Information- Out of every 100 widgets produced 3 will be defective. Using Unitary method We…

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 group has 10 men and 7 women. If 6 people are selected for a committee so that the majority of the…

A: Total number of people are 10+7=17 For the committee to be made with majority women, number of…

Q: in a physiology class, a student must dissect three different specimens. The student can select one…

A: This question can be solved using the concept of combination.

Q: How many different ways can the golf pro at a golf club select a foursome consisting of 1 man and 3…

A: Given,   Number of males = 8 Number of females = 11   The objective is to find how many different…

Q: A club with 20 women and 17 men needs to form a committee of size six. How many committees are…

A:

Q: A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4…

A: Let x be the number of $2 6 packs, y the number of $3 12 packs and z be…

Q: A roller coaster has 3 trains with 8 rows per train. Riders stand in rows of 4, for a total of 32…

A: A fraction is a number in the form xy (where x and y are both integers and y≠0). In the above number…

Q: In a class, there are 4 students majoring in computer science, 9 students majoring information…

A:

Q: A dog shelter is giving away 16 different dogs, but you have room for only six of them. How many…

A: A dog shelter is giving away 16 different dogs. And there is room for only six of them.

Q: An equestrian club has ten members. If the club wants to select a president, vice president, and…

A:

Q: A person buys 32 one-liter bottles of soda bottles for a large company party. The store clerk offers…

A: given : total number of bottles = 32  bottles held by 1 cardboard case = 8 to find : number of…

Q: Three married couples have bought 6 seats in a row for a concert. In how many ways can they be…

A: The number of arrangement in a row is n!.

Q: 2. In your drawer, there are 4 identical pairs of brown socks and 8 identical pairs of green socks.…

A:

Q: An ice cream store sells two drinks in four sizes and has five flavor add ons. In how many ways can…

A: From the provided information, The ice cream store sells two drinks in four size and has five flavor…

Q: How many ways can 12 people line up if Joey and Sally must be next to each other?

A: here given group of 12 people arrange in raw   and arrange around round table

Q: Suppose that I have 250 pieces of candy, I randomly pick 15 of them from the bar and so over that 6…

A:

Q: A fan of country music plans to make a custom CD with 12 of her 25 favorite songs. How many…

A: Given dataTotal songs N = 25 No of combinations for size 12 is given by

Q: A club with 25 members is selecting a committee of 6 people. In how many ways can this be done?

A: *concept:- use defination of Combination.

Q: 2. In a basketball league consisting of 10 teams, each team plays each of the other teams exactly…

A:

Q: A traveling agent has to visit four cities, each of them five times. In how many different ways can…

A: There are 205! 5! 5! 5!ways to visit 4 cities, each of them 5 times.

Q: In a cohort of 25 graduating students, there are 3 different prizes to be awarded. If no student can…

A:

Q: At a charity benefit with 33 people in attendance, three $50 gift certificates are given away as…

A:

Q: How many different bowls of ice cream can you make with 6 flavours and 5 scoops such that you have…

A: Given: Number of flavors=6 Number of scoops=5

Q: How many children are there in a family wherein each girl has as many brothers as sisters, but each…

A: Let assume Number of sister = x Number of brother = y

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 clerk at a bookstore is restocking a shelf of the best-selling novels. He has two copies each of…

A: Part 1: The total number permutations in which 6 books can be arranged is 6! Since there are three…

Q: There are 3 apples, 5 pears and 4 oranges in a basket. If a waiter were to line up these fruits side…

A: There are 3 apples, 5 pears and 4 oranges in a basket. Total fruits = 3+5+4 = 12 n distinct objects…

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

A:

Q: A small company that manufactures juggling equipment makes seven different types of clubs. The…

A: here we have to find the number of ways in a juggler can select 4 types of clubs out of the 7 types…

Q: In a 10 team tournament, trophies are to be given to the top 3 places. In how many ways can the…

A: Given: There are 10 teams in the tournament and trophies are to be given to the top 3 places. Find…

Q: A fast-food restaurant offers a special luncheon menu consisting of a sandwich, French fries, and a…

A: Given, A fast-food restaurant offers a special luncheon menu consisting of a sandwich, French fries,…

Q: A dance club needs 3 new members. If there are 5 males and 9 females applicants, in how many ways…

A: Solution

Q: A fan of country music plans to make a custom CD with 14 of her 26 favorite songs. How many…

A:

Q: A teacher and his eleven students are standing in a single file line waiting to enter the cafeteria…

A: We have given that a teacher and his eleven students are standing in a single file line waiting to…

Q: Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways…

A:

Q: A philanthropist, on his free day, seeks to visit an orphanage from the seven orphanages he supports…

A: Given information No of orphanages = 7 No of elementary school = 10 No of care homes = 8

Q: You baked seven cupcakes of different flavor. In how many ways can you  give two cupcakes each to…

A: Here Given  Total No of cupcakes=7 No of given to each friends=2 No of cupcakes keep with himself=1

Q: How many different ways can a visiting nurse visit 10 patients if she wants to visit them all in one…

A: A visiting nurse can visit 10 patients in 10! ways in one day.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.