B) In an exam, students must answer 9 questions out of a total of 12 and must include exactly 5 of the first 6 in how many ways can they solve the exam?

Q: I am three times as old as my son.Five years later,I sall be two and half time as old as my son.How…

A: In the question, I am three times as old as my son Five years later,I sall be two and half time as…

Q: How many three-digit numbers can be formed of the digits 1, 2, 3, 4, 5, and 6 if each digit can only…

A: There are 6 numbers. The required three digit numbers can be formed using the numbers 1, 2, 3, 4, 5,…

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: In how many ways can a student answer 5 out of 8 questions if he is required to answer 3 of the…

A: Here use combination

Q: In a mathematics examination, a student may select 7 problems from a set of 10 problems. In how may…

A: In a mathematics examination, a student may select 7 problems from a set of 10 problems

Q: 3. A box contains 60 yellow marbles, 110 blue marbles and 90 green marbles. If you pick one marble…

A:

Q: Solve each problem completely. 1. How many committees can be formed with 3 male and 4 female from 5…

A: The Permutation is the method that used to understand the number of possible arrangements with order…

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: How many 6-places license plates are possible if he first 3 places re to be occupied by letters and…

A: Given data: How many 6-places license plates are possible if he first 3 places are to be occupied by…

Q: How many ways are there to fly from City 1 to City 4 with one stop?

A: Here use given table for no of ways fly from city 1 to city 4

Q: How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5 if each digit can be…

A: given digits;  0, 1, 2, 3, 4, and 5 total number of digits = 6 number of four-digits numbers can be…

Q: a) How many three-digit numbers less than 700 can be made using the digits 9, 7, 4, and 2? (Each…

A:

Q: A is two years old older than B who is twice as old as C. If the total of ages of A, B, & C be 27,…

A: Let the age of C  be x . Then B's age and A's age are 2x and x respectively.Then formulate an…

Q: 2. A group of hikers has a trek of 6days to reach Mt. Apo. They traveled 15kms. on the 1s* day,…

A: Any sequence is an arithmetic sequence, if the common difference between consecutive terms is a…

Q: Each student at State College has a student I.D. number consisting of seven digits (the first digit…

A: no.of digits ( 0 to 9)=10no.of letters(A,B,C,D,E)=5

Q: Each student at State College has a student I.D. number consisting of five digits (the first digit…

A:

Q: The average age of a group of six men is 42.If the youngest man leaves , the new average is 46. What…

A:

Q: A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits 0 to 9 How many…

A: It is given that, a small combination lock on a suitcase has 4 wheels, each labeled with the 10…

Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: How many​ 10-digit telephone numbers​ (area code+​number) are possible if the first digit cannot be​…

A:

Q: A baseball team won two out of their last four games. In how many different orders could they have…

A: A baseball team won two out of their last four games. The objective is to find out in how many…

Q: How many ways are there to distribute 20 cents to n children and one parent if the parent receives…

A: Given:-          (a) The children receive any amounts: i. When parents receive a nickel = 5 cents…

Q: If the first chapter of a certain book is 30 pages long and makes up 10% of the book, how many pages…

A: Given that, the first chapter of a certain book is 30 pages long and makes up 10% of the book.

Q: Solve the problem using combination formula. 1. In how many ways can a coach choose three swimmers…

A: The factorial of an integer n is the multiplication of all integers from 1 to n. It is represented…

Q: With a short time remaining in the day, a delivery driver has time to make deliveries at 5 locations…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: Each student at State College has a student I.D. number consisting of 5 digits (the first digit is…

A: Given: Student ID consists of 5 digits and 3 letters. It means that total characters in student ID…

Q: A small combination lock on a suitcase has 3​wheels, each labeled with the 10 digits 0 to 9. How…

A:

Q: How many three-digit numbers can be formed from the digits 1, 2, 3, 5, and 6, if each digit can be…

A:

Q: 6. Number of ways a person can travel from A to C via B, if there are 3 routes from A to B and 5…

A: Let there are 3 places A, B and C. And given that there are 3 routes from A to B. And 5 routes from…

Q: In how many ways can a team of 5 people be formed from a group of 5 Germans, 3 French, and 4…

A: Such prolems can be solved by using permutation .formula used in permutation is:-Prn=n!(n-r)!where…

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

A:

Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: you are to form a 5-digit number from the digits 1, 2, 3, 4, 7, 8, and 9, using each at most once.…

A: Given information- We have given the digits = 1, 2, 3, 4, 7, 8, 9 We have to form 5-digit number…

Q: The results of an interview of 200 students indicate that 89 like GE Math; 77 like GE Arts; 77 like…

A:

Q: At a meeting between coworkers, the eight participants sit on a round table facing the beach. There…

A: Given: There are 8 participants 2 pairs are to be seated together

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: A student is told to work any 8 out of 15 questions on an exam. In how   many different ways can he…

A: He will pick a group of questions. The arrangement will not matter, so we will use the combination…

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

A: Given information: Total teams=10 Each team of the other teams exactly three times.

Q: How many ten-digit telephone numbers are possible if the first three digits must all be different?

A: Given,total no.of digits=10  (0 to 9)

Q: If there are 3 roads from Town A to Town B and 4 roads from Town B to Town C, in how many ways can…

A: there are 3 ways to go from A to B  4 ways to go from B to C  3 ways to go from C to B as we can not…

Q: You are to form 3-digit numbers from the digits 1 to 5. How many 3 digit numbers can be formed if a)…

A: Solution of given question is written in below steps.

Q: Solve the following: 11)  A committee of 6 officials is to be chosen from 8 men and 7 women. If the…

A:

Q: With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different…

A:

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many if he must answer exactly 3…

A: It is an important part of statistics . It is widely used .

Q: Tina must select and answer in any order five of ten essay questions on a test. In how many ways can…

A: Given - Tina must select and answer in any order five of ten essay questions on a test. To find - In…

Q: 8. Each bag to be loaded onto a plane weighs either 12, 18, or 22 pounds. If the plane is carrying…

A: The weight of the lightest bag is 12 pounds   Lighter the weight of the bad more the number of bags…

Q: How many ways can 3 men and 4 women be seated on a bench if the women to be together?

A:

Q: In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak…

A: In a group of 100 persons, 72 people can speak English and 43 can speak French.     To find :- How…