1. Find the number of ways of 6 objects; say a, b, c, d, e, ƒ, taken three at a time. In other words, find the number of "three letter words" with distinct letters that can be formed from the above six letters.

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: Suppose we want to choose 5 objects, without replacement, from 16 distinct objects. (a) If the order…

A: In this question, we want to find the number of ways if the order of choice is relevant and not.…

Q: Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are…

A: Given:- total books =10 maths books =4 Chemistry books =3 history books =2 song lyric book =1

Q: Suppose there are 6 roads connecting town B to town C and 4 roads connecting town C to town D. In…

A: According to the given information in this question  Here are 6 roads connecting town B to C  And 4…

Q: (a) In how many ways can one component of each type be selected? (b) In how many ways can components…

A:

Q: In how many ways can seven people A, B, C, D, E, F and G be seated around a circular table, if A, B,…

A: Hello! As you have posted 4 different questions, we are answering the first question. In case you…

Q: c) There are 18 boys and 13 girls in an English class. During class, there is time for 6 students to…

A:

Q: IV How many different number plates for cars could be made if each number plate contains four (4) of…

A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

Q: In how many ways can a committee of five men and four women be formed from a group of six men and…

A: The number of ways can a committee of five men is 6C5.The number of ways can a committee of four…

Q: Assume that the candle manufacturer has 7 types of round candles and 5 types of square candles…

A: Permutations and combinations: When one has to choose among a set of objects or people, then…

Q: Find the number of arrangements of the letters of the word PENCILS if there are 3 letters between E…

A: Given word: PENCILS Concept: Condition is that there should be 3 letters between E and I. Here first…

Q: a. In how many ways can the letters of the word 'CORPORATION' be arranged so that the vowels always…

A: here use counting principle

Q: 15. How many different arrangements of ten cars in order are possible in a parking lot that is made…

A: Answer:

Q: 1. The plate number system for the four-wheeled vehicles in the country of Dominian consist of 3…

A: 1) Given Information: The plate number consists of 3 letters and 4 digits. The first letter…

Q: 1. If Peter Piper picks 4 baskets of peppers on day one, 7 baskets on day two, and each day…

A: 1. Given peter Piper picks 4 baskets on day 1, 7 on day 2 and 3 more than the previous day…

Q: A 4-person grievance committee is to be selected out of 2 departments, A and B, with 16 and 20…

A: We have to solve

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: A committee of size 6 is being formed from a group of 10 Republicans, 8 Democrats and 4…

A:

Q: In how many ways can a committee of three men and two women be formed from a group of six men and…

A: Given, A group of 6 men and 9 women. To find: Number of ways to formed a committee of 3 men and 2…

Q: Assume that a grade of A,B,C,D, or F is assigned to each of 9 students. In how many ways can grades…

A: From the provided information, The grades are A, B, C, D or F Total students = 9

Q: A teacher requires a student to answer 5 out of 10 questions, without regard to order. How many ways…

A: Number of ways to choose r items out of n items is given by formulae: nCr Here C represents…

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: In how many ways can a bag of three identical balls and four identical coins be formed from a group…

A: Given: Total number balls =12 Total number coins =12

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: From a group of 4 men and 5 women, how many committees of size 3 are possible a) With no…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: Answer the following: a) How Many ways can a stylist arrange 5 of 8 vases from left to right in a…

A: The given questions are related to permutations. The formula is given by nPr=n!(n-r)!

Q: 2. There are 4 different mathematics books and 5 different science books. In how many was can the…

A: Given : There are 4 different mathematics books and 5 different science books. In how many was can…

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: In how many ways can a committee of three men and four women be formed from a group of 10 men and 10…

A:

Q: 10. If there are 15 people and only 2 chairs are available, in how many ways can they be seated?

A: Explanation: Given that,  Number of people=15 Available chairs=2     Formula Used: Crn=n!r!·(n-r)!

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

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

Q: A committee of size 5 is to be chosen from a group of 6 men and 7 women. (a) How many different…

A: Given that 6 men and 7 women. Total people = 6 + 7 = 13

Q: From a group of 4 men and 5 women, how many committees of size 3 are possible a) with no…

A: Since , there are a group of 4 men and 5 women. Therefore , the total number of people=n=4 men + 5…

Q: In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are…

A: As per guidelines expert gave to answer first question only

Q: Assume that a grade of A, B, C, D, F, or NC is assigned to each of 10 students. In how many…

A: Given ,Grades are  A, B,C,D,F or NCTotal grades = 6No. of students = 10

Q: 10 assume that the number of production defects is 26 and that 12 of these are classified as major…

A: Given data, Number of production defects = 26 Number of major defects = 12 Number of design defects…

Q: i How many three-digit phone prefixes that are used to represent a particular geographic area (such…

A: here use combination and permutation

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: Given a class of 12 girls and 10 boys. In how many ways can a committee of five consisting of at…

A: Given aclass of 12 girls and 10 biys

Q: 4. Consider a bag containing four red marbles, two green ones, one transparent one, three yellow…

A: Given that there are 4 red marbles, 2 green,1 transparent, 3 yellow, and 2 orange marbles. So there…

Q: In how many ways can a committee of three men and four women be formed from a group of 12 men and 12…

A: given: Number of men = 12 Number of women = 12 The number of ways of choosing "r" from "n" is…

Q: In how many ways can a PICE chapter with 30 directors choose a president, a vice president, a…

A:

Q: Assume a boat sends signals by arranging six colored flags on a vertical flagpole. If there are two…

A: There are six colored flags on a vertical flagpole out of which two are red and four are green.

Q: In how many ways can a group of eight persons arrange themselves around the circular table?

A:

Q: In how many ways can a committee of two men and three women be formed from a group of nine men and…

A: In how many ways can a committee of two men and three women be formed from a group of nine men and…

Q: In how many ways can a committee of three men and four women be formed from a group of eleven men…

A: Given,no.of mens=11no.of womens=10

Q: 3. A contractor wishes to build 9 houses, each different in design. In how many ways can he place…

A: From the given information, Total number of hoses to be build (n) =9 One side has 6 lots and other…

Q: In how many ways can a committee of 4 men and 5 women be formed from a group of 12 men and 8 ​women?

A: nCr=n!r!(n-r)!

Q: In how many ways can a committee of four men and three women be formed from a group of eight men and…

A: