M&M’s® offers customers the opportunity to create theirown color mix of candy. There are 21 colors to choose from,and customers are allowed to select up to 6 different colors.How many different color mixes are possible, assuming thatno color is selected more than once and 6 different colorsare chosen?

Q: The 23 colleges of interest to a high school senior include 4 that are expensive (tuition more than…

A: Solution

Q: Two coins are randomly drawn from a coin pouch. If there are 5 dimes, 2 nickels, and a quarter, how…

A: As given there are 5 dimes, 2 nickels, and a quarter in a pouch. 1 nickel = 5 cents 1 dime = 10…

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: A bride is choosing a dress for her bridesmaids. If there are 2 styles, 5 colors, and 3 fabrics, in…

A: Given that  A bride is choosing a dress for her bridesmaids. Number of styles = 2 Number of colors =…

Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 2 nickels, and a quarter, how…

A: The pouch contains 4 dimes, 2 nickels and one quarter. Two coins are randomly drawn from a pouch.

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: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 3 nickels, and a quarter, how…

A: The probability density function of X is obtained below:From the given information, number of coins…

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

A:

Q: Suppose we want to choose 2 colors, without replacement, from the 4 colors red, blue, green, and…

A: Given No. of colors = 4 ( i.e, Red, Blue , Green & Purple)a) Arrangement of elements in a…

Q: Elvis has 12 close friends. How many different combinations of 5 of them may be invited for dinner…

A: Total number of friends = 12 Number of friends she can invite = 5

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: 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: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25 (b)…

A:

Q: Suppose a class has 15 males and 17 females and a committee of size 7 is required. How many ways can…

A: Solution

Q: 3) Mr. Rodriguez needs to select 9 players for his basketball team. There are 20 available players .…

A: Given Total players = 20 We need to select 9 out of 20.

Q: At the horse races (with ten horses competing), in how many ways can the top three places be…

A: Permutation: The number of different arrangements of ‘r’ elements from a set of‘n’ elements is…

Q: If you roll to fair dice (one black die and one white die), in how many ways can you obtain a 6 on…

A: # If you roll to fair dice (one black die and one white die), in how many ways can you obtain a 6 on…

Q: A family has 4 children.  How many different boy/girl orders are possible?

A: When a family has a child there are two possibilities either a boy or a girl.

Q: A food company is testing 4 chocolate chip​ cookies, 5 ​crackers, and 6 ​reduced-fat cookies. If…

A: Given : chocolate chip​ cookies : 4 crackers: 5 reduced-fat cookies: 6

Q: A box contains two black balls, labeled 1 and 2, and five white balls, labeled 3, 4, 5, 6, and 7.…

A: One person to get the both balls by 2 different ways

Q: 2. In how many different ways can they arrange to give everybody a chance to experience the ride?

A: Number of people=7, number of bike available=4. To find the number of ways of arrangements so that…

Q: If you roll to fair dice (one black die and one white die), in how many ways can you obtain a 2 on…

A:

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 6 different…

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 bride is choosing a dress for her bridesmaids. If there are 3 styles, 4 colors, and 5 fabrics, in…

A: Given that, Number of styles = 3 Number of colors = 4 Number of fabrics = 5

Q: A classroom has 8 vacant chairs, 3 in the front row and 5 in the back row. In how many ways can 5…

A: Let us assume there are three students A, B and C sitting beside each other. The different ways in…

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 5 colors, and 4 fabrics, in…

A: Given: Styles = 3 Colors = 5 Fabrics = 4 The number of ways that she can select the bridesmaids…

Q: You are teaching a math class, and have seventeen students who are so hard-working and invested, you…

A: Combination: The number of different selections of ‘r’ elements from a set of ‘n’ elements is…

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: 6. From a pool of 10 candidates, a company has to choose a president, vice president and a…

A:

Q: A species is known to have 1) red, brown, black, or grey hair, 2) yellow or white sclera, 3) a pink…

A: For any particular phenotypic combination in the species,       For hair, 4 options are available.…

Q: In a shipment of  62 vials, only 14 do not have hairline cracks. If you randomly select 3 vials from…

A: The number of vials is 62. The number of vials selected randomly is 3.

Q: A rental car company has 14 available cars while on its lot and 3 customers waiting in the office.…

A:

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 8 different…

A:

Q: There are 3 vacancies on the scholarship committee at a certain university. In order to balance the…

A: From the provided information, There are 3 vacancies on the scholarship committee at a certain…

Q: In how many ways can a person choose three movies to watch from a collection of 7 suggested movies?

A: The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

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

A:

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: The 23 colleges of interest to a high school senior include 4 that are expensive (tuition more than…

A:

Q: The Mars company offers customers the opportunity to create their own color mix of M&M’s candy.…

A: It can be calculated by using combination formula  C(n,r)=n! /(n−r)!(r)!

Q: The Choi family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There…

A: Explained below

Q: As a member of a dance troupe, Anita has a costume wardrobe that consists of 2 pairs of tights (1…

A: Given: Anita has a costume wardrobe that consists of 2 pairs of tights (1 white and 1 black), 3…

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 a group of 10 boys and 15 girls how many selections of 6 students are possible?

A: There are 10 boys and 15 girls The total number of students is 25 The total number of ways 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: Consider a Little League team that has 15 players on its roster. Suppose 6 of the 15 players are…

A: Given information: The total number of players in the team is N = 15. The number of left-handed…

Q: in how many ways can 2 men, 4 women, 3 boys, and 3 girls be selected from 6 men, 8 women, 4 boys,…

A: Ans# Given 6 man, 8 women, 4 boys and 5 girls.          How many ways can 2 men, 4 women, 3 boys and…

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

A:

Q: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6…

A:

Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

A:

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.