Permutation or Combination?
A committee of 7 consisting of a chairman, vice chairman, a secretary, and 4 other members is to be chosen from a class of 20 students. In how many ways can this committee be chosen?
b
From 5 consonants and 4 vowels, how many words can be formed using 3 consonants and 2 vowels?
b
Given 7 consonants and 4 vowels, how many 5-letter arrangements can be made if each arrangement consists of 3 different consonants and 2 different vowels?
b
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
c
A polygon 7 sides.How many diagonals can be formed?
c
A research team of 6 scientists is to be chosen from 10 chemists, 14 biologists, and 12 physicists. How many possible research teams could be formed containing at most 1 physicist.
c
A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?
c
Barry owns 5 dogs and he is taking 3 of them out for a walk.
c
Brandon wants to take 3 dogs with him on his morning walk. If Brandon owns 8 dogs, how many different groups of dogs can he choose for his walk?
c
Determine the number of four card hands that contain at least 2 clubs.
c
From 8 men and 5 women, a committee of 4 is selected. How many groups will have 3 women and 1 man?
c
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
c
How many committees are possible if 5 people are chosen from 30?
c
How many ways are there to deal a five-card hand consisting of three eight's and two sevens?
c
How many ways can 3 CDs be selected from a collection of 10 CDs?
c
How many ways can two books be picked from a list of six?
c
How many ways can two cards be chosen from a deck of 52?
c
How many ways can two puppies be chosen from a litter of five?
c
If ten people shake hands with each other only once, What is the total number of handshakes?
c
In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?
c
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
c
In a group of 9 people, there are 4 females and 5 males. Determine the number of 4-member committees consisting of at least 1 female that can be formed.
c
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
c
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
c
In how many ways can a poker player obtain a 5 card hand that contains exactly three aces?
c
Jessica is packing her bags for her vacation. She has 8 unique tigers, but only 4 fit in her bag. How many different groups of 4 tigers can she take?
c
Michael is packing his bags for his vacation. He has 6 unique socks, but only 5 fit in his bag. How many different groups of 5 socks can he take?
c
Order does not matter
c
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
c
Selecting three students to attend a conference in Washington, D.C.
c
The Gamma Zeta Beta fraternity must choose a committee of four members to plan its annual Children's Hospital fund raiser and beer bash. If the fraternity has 10 members, how many different committees can be chosen?
c
The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and at least 4 bowlers?
c
The number of quadrilaterals that can be formed using six distinct points on the circumference of a circle is...?
c
Vanessa is packing her bags for her vacation. She has 5 unique action figures, but only 3 fit in her bag. How many different groups of 3 action figures can she take?
c
You are selecting 2 appetizers from a restaurant menu consisting of 4 appetizers.
c
You have 4 different sweaters and you are going to bring 2 of them along with you on a trip.
c
You have 8 friends, and you will select 2 of them to go to a movie with you, since you have 2 extra tickets.
c
You just got a free ticket for a boat ride, and you can bring along 2 friends! Unfortunately, you have 5 friends who want to come along. How many different groups of friends could you take with you?
c
6 students are competing in a race; the first place, second place, and third place ribbons will be handed out to three students.
p
A photographer is arranging a family of 6 people in line for a photo.
p
Assigning students to their seats on the first day of school.
p
At the start of the year, a new teacher is making a seating plan for her class. If there are 20 students in her class, how many seating plans could she make?
p
Determine the number of grad-committee executives consisting of a President, Vice-President, Treasurer and Secretary that can be formed from a group of 15.
p
How many passwords can be made using the letters A, B, C, D, E, and F? (Using each letter only once)
p
How many ways can 3 people be seated on 5 chairs?
p
How many ways can a baseball manager arrange the batting order of nine players?
p
How many ways can you arrange 8 cars?
p
If you have 6 New Year greeting cards and you want to send them to 4 of your friends, in how many ways can this be done?
p
In a club of 30 members, how many ways can a president and vice president be chosen?
p
In a ten horse race, how many ways can the horses come in first, second, and third?
p
In how many different ways can five persons stand in a line for a group photograph?
p
In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?
p
Order matters
p
Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?
p
The Gamma Zeta Beta fraternity is electing a President, Vice President, Secretary, and Kegger Chair. If the fraternity has 10 members, in how many different ways can the officers be chosen?
p
You own 7 different books and are arranging them on a shelf.
p
You received 5 Christmas cards and you want to arrange them on the single level shelf above your fireplace.
p
How many three digit numbers can you make with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9?
p
Selecting a lead and an understudy for a school play.
p
There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf?
b
How many schedules can be made if 6 classes are chosen from a list of 25?
p
In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?
p
Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?
p
