List of top Mathematics Questions on Permutations and Combinations

Coefficient of \(x^{10}\) in the expansion of \[ \left(x^2+\frac1x\right)^{12} + \left(x+\frac1{x^2}\right)^{12} \] is:
If \( n = 5 \) and \( r = 3 \), then the value of \( ^nP_r \) is:
A person has two parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?
There are 9 different rock lizard species, each with a unique colour. Lizards of 2 different species sit on a rock at any given time. The number of possible colour combinations of rock lizards seen together on a rock is:
From the word ARRANGEMENT, how many distinct 9-letter words can be formed?
How many 4-digit numbers can be formed using digits 1 to 6 if the digit 4 is never there in the number and the repetition of digits is not allowed?
Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is:
Number of three digit numbers that can be formed using 0, 1, 2, 3, and 5 where these digits are allowed to repeat any number of times, is equal to:
There are 9 different rock lizard species, each with a unique colour. Lizards of 2 different species sit on a rock at any given time. The number of possible colour combinations of rock lizards seen together on a rock is:
Out of eight crew members, three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?
A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
The number of three-letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is
A company CEO invited nine persons for a business meeting, where the host will be seated at a circular table. How many different arrangements are possible if two invitees X and Y be seated on either side of the host CEO?
Find the number of ways in which ten different flowers can be strung together to make a garland in such a way that three particular flowers are always together?
A committee of 3 experts is to be selected out of a panel of 7 persons. Three of them are engineers, Three are managers and, one is both engineer and manager. In how many ways can the committee be selected if it must have atleast one engineer and one manager?
A cricket team of 11 players is to be formed from a pool of 16 players that includes 4 bowlers and 2 wicket-keepers. In how many different ways can a team be formed so that the team has at least 3 bowlers and wicket keeper?
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs X refuses to serve in a committee if Mr Y is its member, is
The number of ways in which four letters of the word MATHEMATICS can be arranged is
Ten different letters are given. Words with five letters are formed from these given letters. The number of words which have at least one letter repeated is
In how many different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged