Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

Q: For this problem, assume that you have a committee of 12 members, and that you must choose a…

A: Given- Assume that you have a committee of 12 members, and that you must choose a secretary, and…

Q: A casting director wishes to find one male and one female to cast in his play. If he plans to…

A:

Q: From a group of 7 women and 8 men a committee consisting of 4 men and 3 women is to be formed. How…

A: Given, 7 women and 8 men committee size 4 men and 3 women

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: Suppose we want to choose 5 letters, without replacement, from 8 distinct letters. (a) If the order…

A: ncr=n!r!n-r! and we will use combination

Q: Suppose we want to choose 3 letters, without replacement, from the 4 letters A, B, C, and D.

A: We want to choose 3 letters and we have 4 letters A,B,C and D, we have to determine (a) How many…

Q: a family wants to adopt 2 cats and 3 dogs from a shelter that has 12 cats and 15 dogs. in how many…

A: The number of ways of selecting 2 cats from 12 cats is,

Q: How many ways can an adviser choose 4 students from a class of 12 if they are all assigned the same…

A: We have to find the number of ways that can an adviser choose 4 students from a class of 12 if they…

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: A senate committee has 15 members.  If a subcommittee of 6 senators is to be formed from the…

A:

Q: Suppose we want to choose 5 letters, without replacement, from 18 distinct letters. (a) How many…

A: (a)   Determine the number of ways that the 5 letters can be selected from 18 distinct letters…

Q: Suppose we want to choose 7 objects, without replacement, from 9 distinct objects. (a) How many ways…

A:

Q: (a) How many ways are there to place 10 paintings into 8 boxes, given there should be at least one…

A: a. The total number of ways of dividing 10 paintings into 8 boxes so at least one painting in each…

Q: A committee of 5 students is to be chosen from 6 boys and 5 girls 2. How many committees will…

A: Given,no.of boys=6no.of girls=5total no.of students=11

Q: Suppose we want to choose  3  colors, without replacement, from the  4  colors red, blue, green, and…

A: It is given that there 4 colors red,blue,green and purple.  and we need  to choose 3 colors without…

Q: Suppose we want to choose 7 letters, without replacement, from 12 distinct letters. (If necessary,…

A: Given,Total no.of letters=12

Q: A company has 10 male and 11 female employees, and needs to nominate 2 men and 2 women for the…

A: They can choose 2 men from 10 men in 10C2 ways They can choose 2 women from 11 women in 11C2 ways.…

Q: How many ways can 7 people be assigned to 1 triple and two double rooms? If only 6 persons will be…

A:

Q: How many different ways can you arrange 10 students (4 students with blonde hair, 2 students with…

A: Total Number of students = 10 Number of students with blonde hair = 4 Number of students with black…

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: How many ways can 2 students be selected from a group of 5 students if order does not matter?

A: Given information- We have given that we have given a group of 5 students. We have to select 2…

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. 1) How many…

A: Provided information is ; number of objects(n) =15 For Case 1] : if the order of the choices is…

Q: Suppose there are 100 cans of green beans in a grocery store, and 75 of these are "Best Deal" brand…

A: There are 100 cans of green beans in grocery store. And 75 cans of these are "Best Deal" brand green…

Q: or this problem, assume that 13 exhibits entered the science fair, and that we want to assign 5…

A: Given Data :  Number of exhibits are 13 in a science fair                        Number of Prizes…

Q: A student has 4 different biology books, 4 different chemistry books, and 5 different physics books.…

A:

Q: How many ways are there to arrange the letters m, n, o, p, and q such that neither m nor n is…

A: There are 5 letters in m, n, o, p, and q. We can arrange them in 5!= 120 ways   If m is followed…

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: Suppose we want to choose 5 objects, without replacement, from 18 distinct objects. a) If the order…

A: Given,Total no.of distinct objects=18

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: How many ways can Carlos choose 2 pizza toppings from a menu of 20 toppings if each topping can only…

A: The number of pizza toppings chosen is 2 and the total number of toppings is 20.

Q: How many ways can A, B, C, and D be arranged to the __ __ __ __ if D is restricted to the third and…

A: Let A,B,C and D be the four letters that we have to arrange. Given: D is restricted to the third and…

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: Suppose we want to choose 5 objects, without replacement, from 17 distinct objects. (a) If the order…

A: We will the number of ways in both conditions as following.

Q: Suppose we want to choose 6 objects, without replacement, from 8 distinct objects. (If necessary,…

A: Given data: Number of distinct objects  (n) = 8 Number of objects to choose(x) = 6

Q: Suppose we want to choose 5 objects, without replacement, from 14 distinct objects. (If necessary,…

A:

Q: Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (a) If the order…

A: Solve

Q: (a) If first prize is $100, second prize is $80, and third prize is $30, in how many different ways…

A: Given: People buy raffle tickets = 200

Q: How many ways are there to stack an ice-cream cone with 4 scoops if the choices are a. cookie dough,…

A: To calculate the total number of ways to take an ice-cream cone with 4 scoops if the choices are…

Q: If you have six books, but there is room for only four books on the shelf, in how many ways can you…

A: From the given information, n=6 and r=4.

Q: 1. A license plate begins with three letters and three numbers. If the possible letters are all…

A: Given: The possible letters are vowels; that is, a, e, i, o, u. The possible digits are odd numbers;…

Q: Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways can…

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Q: In how many ways can we choose 5 students from 7 boys and 5 girls?

A:

Q: 3. Marty is a bookworm and he has various collections of novels, series and other story books. If he…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In how many ways can two admirals, three generals, and four lieutenants can be seated in a row of…

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Q: A company has 7 male and 12 female employees, and needs to nominate 2 men and 2 women for the…

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Q: In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must…

A: We have to find the possible number of ways to form a committee of 5 members from 5 juniors and 7…

Q: In how many ways can Mrs. Smith give a chocolate bar, a bag of potato chips, and a can of cane juice…

A: Mrs. Smith give a chocolate bar , a bag of potato chips and can of cane juice to 3 of the 21…

Q: How many ways are there to stack an​ ice-cream cone with 4 scoops if the choices are   a.…

A: For flavours must be different then once used flavour can't be used next time. So in first stack we…

Q: If there are five different toy cars, and you want to put fifteen toy cars on the display, how many…

A: Permutation is the measurement of principle counting. It is measure that arrange the data in an…