List of top Quantitative Aptitude Questions on Permutations and Combinations

In how many ways can the letters of the word 'PERMUTATIONS' be arranged if vowels are together?
In a group of children, each child gives a gift to every other. If the number of gifts is 132, then the number of children is:
The number of selections of six persons including only one teacher from 4 teachers and 7 students is:
The number of selections of four letters from the letters of the word ASSASSINATION is:
In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is
In how many ways can 2 students be chosen from the class of 20 students?
From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.
In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
The average length of three tapes is 6800 feet. None of the tapes is less than 6400 feet. What is the greatest possible length of one of the other tapes?
The times taken by a phone operator to complete a call are 9, 2, 3, 1, 5 minutes respectively. What is the average time per call?
The average salary of 3 workers is 95 Rs. per week. If one earns Rs.115 and the second earns Rs.65, how much is the salary of the 3rd worker?
In how many ways can a cricket eleven be chosen out of a batch of 15 players?
In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?
In how many ways can 5 different books be arranged on a shelf if two particular books must be together?

The number of ways to arrange 5 distinct books on a shelf is: 
 

Find the number of ways to arrange 6 distinct books on a shelf if 2 specific books must be adjacent.
In how many ways can 5 distinct letters be arranged in a circle?
There are 4 roads between towns A and B, and 3 roads between towns B and C. How many different ways can a person travel from A to C via B and return to A without using the same road more than once in each direction?

In a seating arrangement, 5 people (A, B, C, D, E) sit in a row. A and B must sit together, and C cannot sit at the ends. How many arrangements are possible? 
 

A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?
Letters of the word “ATTRACT” are written on cards and kept on a table. Manish lifts three cards at a time, writes all possible combinations of the three letters on a piece of paper, and then replaces the cards. He is to strike out all the words which look the same when seen in a mirror. How many words is he left with?
Rajat draws a \(10 \times 10\) grid with squares numbered 1 to 100. He places two identical stones on any two separate squares. How many distinct ways are possible?
In a factory making radioactive substances, it was considered that three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in the company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of 5?