A student must take 4 courses. In how many ways can they do that if there are 8 courses and 1 is mandatory

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: We have given that,  Number of Democratic senators = 69 Number of Republican senators = 31

Q: if there are no restrictions? if Holly and Sam cannot sit together?

A: here given ,  Holly, Parker, Jace, Ola, Amir and Sam have gone out to a football game together, They…

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: You need to create a new passcode for your iPhone, their are 10 numbers to choose from and your…

A: Remark: We know the number of different permutations of n distinct objects taken r at a time is nPr…

Q: How many ways are there to stack an ice-cream come with 4 scoops if the choices are pistachio,…

A: The choices are pistachio, peach, cherry, walnut, peanut butter, and raspberry. That is 6. I scoop…

Q: There are 2 copies each of 4 different books. In how many ways can they be arranged on a shelf?

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Q: A woman has ten skirts and five blouses. Assuming that they all match, how many different…

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Q: A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be…

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Q: Of 10 possible books, you plan to take 4 with you on vacation. How many different collections of 4…

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Q: How many ways can we assign 124 students to 4 sections in such a way that Section 1 must have at…

A: Given: There are 124 students and 4 sections Section 1 must have at least 30 students, section 2…

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

A: Given that In how many ways can two admirals, three generals, and four lieutenants can be seated in…

Q: There are three boys and three girls at a party. In how many ways can they be seated if they can sit…

A: Given, There are three boys and three girls at a party they can sit down three at a time

Q: In a bag containing 5 white balls and 6 black balls, how many ways can we draw a white or a black…

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Q: Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee…

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Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: You have 5 Math books, 2 History books, and 4 Science books. How many ways are there to arrange the…

A: If there are n number of distinct objects out of which r objects are selected and then arranged then…

Q: There are 9 female board members and 21 male board members. How many ways are there to make a…

A: We use combination to find number of way to make a committee.

Q: Six math books, four physics books and three chemistry books are arranged on a shelf. How many…

A:

Q: If I have 9 flower pots and 11 different flowers how many different ways can flowers be in each pot?

A: 11C9 ways. that is in 55 way.

Q: Federal Express driver must make ten deliveries to ten different addresses. In how many ways can she…

A: factorial of n items gives you the number of ways you can arrange the given items

Q: A club with 5 members is to choose 3​ officers: ​ president, vice-president, and​…

A:

Q: The board of directors corporation must select a president, secretary, and a treasurer. In how many…

A: Given Data: The total number of members is: n=25 There are three members required a president,…

Q: In how many ways can four boys and five girls sit in a row if the boys and girls must sit…

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Q: A club with 17 members must choose a president, a vice president, a treasurer, and a secretary. How…

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Q: There are 5 boys and 5 girls at a party. In how many ways can they be seated in a row if they must…

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

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Q: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

A: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

Q: The 50 members of a club include both the club president and the club treasurer. All 50 members want…

A: Topic- permutations and  combinations

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: There are 10 doors to a coliseum. In how many ways can a person go in and out if one can enter any…

A: There are 10 doors to a coliseum . A person can go in in 10 ways.

Q: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. How many…

A: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. We need to…

Q: In a​ bag, there are 6 purple and 12 green marbles. If you reach in and randomly choose 5 ​marbles,…

A: Given, there are 6 purple and 12 green marbles in a bag To find the number of ways to choose exactly…

Q: A combination lock uses 4 numbers, each of which can be 0 to 36. If there are no restrictions on the…

A: Here, it can be observed that all numbers are independent of each other.

Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: From the provided information, There are 13 female board members and 17 male board members. Total…

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: Suppose a library has at least 6 copies of mathematics book, at least 6 copies of a physics book,…

A:

Q: If there are 5 ways to perform task A and 6 ways to perform task​ B, then how many ways are there…

A: Given information No of ways to do task A = 5 No of ways to do task B = 6

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 30 members. In how…

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Q: Assume that the camper has 5 jackets, 3 sleeping bags, and 14 different packages of food. An outfit…

A: Combination is the way of selecting a units from a set without considering position of order. The…

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: Combination Rule:A combination is a selection of all or part of a set of objects, without regard to…

Q: A) 15 people are playing soccer, only 3 people know how to be a goalkeeper, how many ways are to…

A: INTRODUCTION :  probability: If a random experiment or a trial results in 'n' exhaustive, mutually…

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

A:

Q: If a family has four children, in how many ways could the parents have two boys and two girls?

A:

Q: A jury of 12 people is to be chosen from 10 men and 12 women. How many ways can a jury of 6 men and…

A: Given problem Given that   A jury of 12 people is to be chosen from 10 men and 12 women.

Q: The board directors of a corporation must select a president, a secretary, and a treasurer. In how…

A: We will use arithmetic method to find solution to the problem.

Q: If a family has seven children, in how many ways could the parents have three boys and four girls?

A: Since there are 7 children. To find the number of ways such that parents have three boys and four…

Q: I have nine books and have room to display only four of them at a time on my bookself. how many…

A:

Q: Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can…

A: To count the number of possible selections

Q: Suppose there are 8 male professors and 5 female professors teaching a Math class. How many ways can…

A: Sum rule principle:   Let E1 denote the first event that an occur in m ways and then E2 denote the…

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.