1. In how many ways can 10 people line up for a bus ticket? Answer: There can be possible ways.

Q: In how many ways can 10 people be seated on a bench if only 4 seats are available?

A: Given problem Given that   In how many ways can 10 people be seated on a bench if only 4 seats are…

Q: How many five-card poker hands containing exactly one pair are possible from a deck of 52 cards?

A: five-card poker hands containing exactly one pair are possible from a deck of 52 cards:

Q: In how many ways can a male president and a male or a female vice-president be selected out of 5 men…

A: To determine the number of ways in which a male president and a male or a female vice‐president be…

Q: In how many different ways can the director of a research laboratory choose two chemical engineers…

A:

Q: 3) In how many ways can three bracelets be selected from a box of ten bracelets?

A:

Q: 10. In how many ways can you line up 5persons to get on a bus?

A: Given problem Given that   10) In how many ways can you line up 5 persons to get on a bus ?

Q: In how many ways can a class of 32 students select four people to serve on a committee?

A: Total number of students in the class (n) = 32 Number of students to be selected to serve on a…

Q: In how many ways can six books be lined up along a shelf?

A:

Q: How many ways may 5 students be elected from a club with 45 members?

A: Total number of students = 45 Number of students to be selected = 5

Q: In how many ways can a class of 19 students be assigned 2 A's, 2 B's, 10 C's, 2 D's and 3 F's?

A:

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that all are…

A: Given: The total number of cards in a deck is 52. The total number of the numbered cards in a deck…

Q: In how many ways can 5 persons be seated in a room where there are 10 seats?

A: We have to find number of ways to seat people in room.

Q: 1. How many different license plates are possible using 3 letters followed by 3 digits? digits and…

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Q: (a) How many different committees of size 3 can be formed from 14 people? (b) From the 13 albums…

A: a) Given, No of people(n)=14 size(r)=3   How many different committees can be formed.

Q: In how many ways can first, second, and third prizes be awarded in a contest with 110 contestants?…

A:

Q: In how many ways can  8 people sit around a round table if two particular people must sit next to…

A: Given  Number  of people =8  We want to find how many ways to 8 people sit around round table if two…

Q: In how many ways can a president, a vice president, a secretary and at reasurer be elected from a…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: 4. Your school is hosting a Mathletes competition in which senior and junior teams will be entering.…

A: Selection of x items from n objects can be represented by combination  Cxn and arrangement of same…

Q: A automobile race contains 15 racecars. In how many ways can the racecars finish in first, second,…

A: A automobile race contains 15 racecars.

Q: 2. If you have 7 types of candy, how many pieces of candy would you have to guarantee that you had…

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Q: In how many ways can 6 bicycles be parked in a row?

A:

Q: In how many ways can 7 students from a class of 28 be chosen for a field trip?

A:

Q: a. How many different ways can the officers be appointed?

A: Given that  A corporation must appoint  A president , Chief executive officer (CEO) , Chief…

Q: In how many different ways can the director of a research laboratory choose two chemists from among…

A: Solution: Given information: Chemists applicants = 11  Physicists applicants = 7   To choose 2…

Q: In how many ways can you invite one or more of your five friends to a party?

A: There are total 5 friends available among which 1 or more than 1 friends can be invited to the…

Q: 3. While they were researching marmosets, a particularly convoluted walk through Wikipedia caused…

A: Total number of letters=28 , which includes  A N T I D S E B L H M R 4 3 3 5 1 4 2 1 1 1 2 1…

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

A:

Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: Question: Anabelle would like to invite 9 friends to go a trip but has room for only 5 of them . In…

Q: (a) If a student must answer 8 of 12 questions on an examination, how many different selections of…

A: Given:  A student must answer 8 of 12 questions on an examination  To find:a) The different…

Q: 4. The Recycling Club collected 196 cans on Monday, 248 on Tuesday, 205 on Wednesday and , 256 on…

A:

Q: (a) How many committees can be formed? (b) How many committees can be formed with at least 2 men?…

A: here total 8 men and 7 women that is 15 employees in office committee of 4 member has to be formed…

Q: 1. The IE Falcons plays 14 games during the COE Basketball Tournament. In how many ways can the team…

A: Note- As per our policy we can answer only 1st question. If you want solutions for other, then you…

Q: In how many ways can we seat 7 people at a round table with a certain 3 people side by side?

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Q: In how many ways can a person choose three movies to watch from a collection of 7 suggested movies?

A: The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: How many ways can five boys and five girls be seated alternately at a circular table?

A: Given: 5 boys and 5 girls are to be arranged in circular way alternately. The diagram can be…

Q: 10 students should be accomodated in two 3-bed and two 2-bed rooms. In how many ways can they be…

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Q: 6. How many ways can my daughter put 50 pairs of shoes on 4 dolls ?

A: It is given that, We have 50 pairs of shoes and there are 4 dolls. We know that if n object can be…

Q: In how many ways can a couple invite 3 out of their 15 closest friends to a dinner party?

A:

Q: n how many ways could a club of 19 members choose a president, vice president, and treasurer?

A: The club has 19 members. To find the number of ways to choose a president, vice president, and…

Q: In how many ways can a student select 7 out of 10 questions to work on an exam?

A: Given that, The total number of question to work on an exam is, n=10 The student select number of…

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

A:

Q: 4. Ms. Green must choose three students from her chess club to speak on the Rebel Report. If the…

A: Given that  Total member=8 She choose member=3

Q: In how many ways can first, second, and third prizes be awarded in a contest with 360 contestants?…

A:

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: 3. How many ways can 7 cards be chosen from a standard deck of 52 cards?

A: In the given problem, we have 52 cards. We have to find the number of ways for which we can choose 7…

Q: 6) The ski club with twelve members is to choose three officers captain, co-captain & secretary, how…

A: To find the number of ways

Q: 2. Forty students in a class took a Mathematics test. If 80% of the students passed the test, how…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 3. A blood bank needs twenty people to help with a blood drive. Twenty-five people have volunteered.…

A: Topic- Permutation and Combination

Q: In how many ways can a class of 32 students select a president, vice president, treasurer, and…

A: Given, Total number of students = 32  Selected students : 1 President, 1 vice president, 1 treasurer…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.