List of top Quantitative Aptitude Questions on Permutations and Combinations

In a certain class, 40\(\%\) of the students take coffee, 40\(\%\) take tea, 50\(\%\) take milk, and 10\(\%\) take all the three. Also, 20\(\%\) take coffee and tea, 20\(\%\) take tea and milk, and 20\(\%\) take coffee and milk. 10 students do not take any of the three. How many students are there in the class?

In a class of 150 students, 55 speak English, 85 speak Malayalam and 30 speak neither English nor Malayalam. How many students speak both English and Malayalam?

A members in a sports academy play one or two or all of the three games – Tennis, Squash, Badminton. 5 members play only tennis, 8 play only squah, 7 play only badminton. Three members play only two games – Tennis and Squash. Four members play only Squash and Badminton. Four other members play only Tennnis and Badminton. Two members play all the three games.
In all how many members play Squash?

Raja divides Rs 8600 among five sons, 4 daughter and 2 grand children. If each daughter receives 4 times as much as each grand children, and each son receives five times as much as each grand children, how much does each son receive?

The vice-chancellor of ABC University decided to form a committee to look into the feasibility of introduction of semester systems at the undergraduate level. Five members from the Executive Council and 7 members from the Academic Council were found to be suitable for the job. In how many ways can the vice-chancellor form the committee of 6 members such that at least 4 members of the committee belong to the Academic Council?

ln how many different ways can the letters of the word 'VINTAGE' be arranged such that the vowels always correctly together

How many integers greater than 999 but not greater than 4000 can be formed with the digits 0, 1,2,3 and 4 if repeatition is allowed

In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. The number of students who passed in Physics only 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?

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 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?

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?

In how many different ways can the letters of the word ‘CREAM’ be arranged?

How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?

In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs doesn’t matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?

How many different subsets of the set {10, 14, 17, 24} are there that contain an odd number of elements?

A committee is to be formed from amongst 9 boys and 6 girls. In how many ways can the boys and girls divide themselves into groups of three so that no group has more than 2 girls and no group has all boys?

There are eight persons – P, Q, R, S, T, U, V and W, standing in a row and four distinct articles A, B, C and D are to be given to four people. No four neighboring persons receive an article. How many ways can this distribution be done?

There are 8 tasks and 8 persons. Task 1 cannot be assigned either to person 1 or to person 2 or to person 8; task 2 must be assigned to either person 3 or person 4 or person 5. Every person is to be assigned one task. In how many ways can the tasks be assigned?