If the 50 guests in the party described in question number 5 where actually couples (so there are 25 couples in the party) and each guest will shake the hand of every other guest. (Of course, no handshake will be exchanged between a guest and his/her partner). How many handshakes were exchanged in the party?

Q: |In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 9…

A: Combination is the arrangement of data without any order. It can arrange data from the sample from…

Q: An insurance agent has a list of 7 prospects and decides to telephone 5 of the prospects today and…

A: we want to find different ways can the agent telephone the prospects

Q: In how many ways can you send a message to your 8 teachers informing them that you have submitted…

A: Query- In how many ways can you send a message to your 8 teachers informing them that you have…

Q: How many different 4-letter radio-station call letters can be made   if the first letter cannot be…

A: Given: 4- letter radio-station call letter has to be made with first letter should not be A, B or C…

Q: Assume that the committee has 14 members, and that 4 different members are to be given special…

A: We have to find probability..

Q: At an assembly, 8 out of the first 20 students who entered the gym were wearing grey shoes. Based on…

A:

Q: If a phone company sends a random 6-digit number to customers to activate their phone, how many…

A: Consider a problem in which there are n vacant inline spots, each spot is to be filled by any of the…

Q: Show that if there are 30 students in a class, then at least two have last names that begin with the…

A: We are given that there are 30 students in the class. We will assume that every student has first…

Q: If there is 1 person in a room and no one shakes his or her hand, and then someone else enters the…

A: Let n be the number of persons in the room.

Q: Given S = {1,2,5,8,9}, in how many 3 digit numbers can be formed if each number cannot be used more…

A: Here given ,  There are total 5 digits are available . And from given 5 digits make 3 digit number…

Q: If 15 people won prizes in the PCSO lottery (assuming that there are no ties), how many ways can…

A: Solution: From the given information, there are 15 people.

Q: If in a convention, 53 people liked coffee A, 52 people liked coffee b, 42 people liked the coffee…

A:

Q: A woman has 11 close friends. (i) In how many ways can she invite 6 of them to dinner? (ii)  In how…

A: Total number of friends are 11.i Number of ways in which she can invite 6 of them.C611=11!6! 5!…

Q: From among the 36 teachers in a college, one principal, one vice-principal and the teacher-in-charge…

A: It is given that there are 36 teachers in a college. We have to appoint one principal, one…

Q: In how many ways: a. Can 8 people be lined up to get on a bus? b. Can they be seated if 4 specific…

A: Total persons  = 8 people a) There are 8 people, there will be 8 places to arrange (here order will…

Q: When the members of a family discussed where their annual reunion should take​ place, they found…

A:

Q: A group of 10 friends go out for dinner at a fancy dining room and they each leave their hat with an…

A: To find In how many ways can the coat room clerk return the hats so that everyone receives the wrong…

Q: If there are 3 representatives from Company A and 4 representatives from Company B meet. If they…

A: This is a application of Fundamental Principle of Counting .

Q: When the members of a family discussed where their annual reunion should take place, they found that…

A: Member would not go to park be n(P)=12 Member would not go to beach be n(B)=10 Member would not go…

Q: If 3 representatives from Company A, 4 representatives from Company and 2 lawyers (from a different…

A: Given data , 3 representatives from Company A , 4 representatives from Company B , 2 lawyers from (…

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: How many four-digit passwords can be made from the digits 0 to 5, if digits can be repeated?

A: From 0 to 5 there are 6 digits.  Given that the digits can be repeated. This means for each digit…

Q: In how many ways can a party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit…

A: Given :A party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each…

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

A: Given, A woman has 11 close friends. To find,  How many ways can she invite 5 of them to dinner if…

Q: In an examination paper, there are 7 questions in part A out of which any 4 are Example 48. to be…

A:

Q: If 10 people come from different places and shake hands in how many different way could this be done

A: The formula for the number of handshakes possible with n people is          handshakes = n*(n -…

Q: 1. There are 5 teenagers and 8 adults available for a 5-p. teenager and one adult, how many possible…

A:

Q: A committee of 5 is to be made from 3 students and 6 teachers. In how many ways can this be done a.…

A:

Q: In how many ways can first and second prize be awarded in contest with 100 people, assuming that…

A: There are 100 students in the contest.

Q: When the members of a family discussed where their annual reunion should take​ place, they found…

A: Given: Shorthand representation NP= Not go to the park NB= Not go to the beach NC= Not go to the…

Q: A  commitee of 2 teachers is to be formed in a school such that there is one male and one female…

A: We can pick a female teacher from 12 female teachers in 12 ways.  We can pick a male teacher from 15…

Q: suppose that ten service customers need service call and the maintenance worker can only service…

A: Consider the given information. Total Number of service customers = 10 Number of services done each…

Q: Assume that the committee consists of 11 members including Cecil. The same three offices are to be…

A: n = 11 members positions = 3 Problem can be solved using the concept of permutation and combination.

Q: There are 15 persons in a party and if each 2 of them shakes hands with each other, how many ways…

A: Given data: 15 persons in a party Each 2 of them shakes hands with each other

Q: In a survey of 60 people, it was found out that 25 read Manila Bulletin, 26 read Philippine Daily…

A: Solution:There is 60 people in a surveylet xbe 25 theread Manila Bulletiny be 26 the read Philippine…

Q: There are 50 guests in a party. If each guest shakes hands with all other guests, how many…

A:

Q: A committe of 5 members is to be formed out of 6 gents and 4 ladies. In how many ways this can be…

A: Given: Total Gents = 6 Total Ladies = 4 Required 5 members committee for the at least two ladies

Q: In how many ways can 3 blue books and 4 red books be arranged on a shelf if a red book must be on…

A: The number of ways in which n different objects can be arranged, is given by n!, where,…

Q: Suppose there are 14 freshman, 13 sophomores, 15 juniors, and 17 seniors running for the offices of…

A: There are 14 freshman, 13 sophomores, 15 juniors and 17 seniors.

Q: What if the jelly bean machine gives 9 jelly beans to the first customer who put in a coin, 13 to…

A: If the initial term of an arithmetic progression is {\displaystyle a_{1}} and the common difference…

Q: From a group of 7 men and 6 women, five person are to be selected to form a committee so that at…

A: Given, No of men=7 No of women=6 Number of people to be selected in a committee  = 5Minimum number…

Q: There are 100 people consisting of 50 married couples in a room. Assuming that no husband or…

A: Solution: The objective is to find how many handshakes in a room.

Q: suppose that five service customers need service call and the maintenance worker can only service…

A:

Q: If 6 out of 30 people over the age of 100 are male, Ho our of 30 people over the age of 100 are…

A: Given that The number of total people=30 Number of male over aged of 100 =6 Then we have to find the…

Q: Of the first 5 vehicles in the teacher’s parking lot last Tuesday, 2 of them were minivans. Based on…

A: 48

Q: From a group of 18 customers, 4 are to be chosen to receive a special gift. Assuming that the order…

A: The number of groups of 4 customers can be chosen is,

Q: If a bank sends a random 5-digit number to customers for security, how many potential numbers are…

A:

Q: Prove that at any party where people are shaking hands, at last two people will have always shaken…

A: Let there are N people at the party so a single person can shake hands with some number between 0…

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

A: