List of top Mathematics Questions on permutations and combinations

If a polygon has 54 diagonals, find the number of sides of the polygon.

The number of numbers between \(345\) and \(543\) such that the sum of the digits in each number is \(15\) is

If \(3\times3\) matrices are formed by using \(0,\pm1,\pm2\) as their elements, then the number of matrices whose trace is \(0\) is

The number of odd factors of \(24!\) is

The number of ways of distributing 5 identical things to 4 persons so that any person may get at most 5 things is:

If all the letters of the word 'ASSOCIATION' are permuted in all possible ways to form all 11-letter words (with or without meaning), then among these words, the number of words in which the identical letters are always together but no two such groups of identical letters are together is:

By using all the letters of the word 'LETTER', all possible 6-letter words (with or without meaning) are formed. If all these words are arranged in dictionary order, then the rank of the word 'TRELET' is:

If \( a \) is the coefficient of \( x^7 \) and \( b \) is the term independent of \( x \) in the expansion of \( \left( \frac{3x^4}{4} - \frac{4}{3x^3} \right)^7 \), then \( \frac{b}{a} = \)

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

The number of 3-digit numbers formed using digits 2,3,5,7,9 without repetition that are divisible by 3 is

There are 7 men and 5 women in a park. The number of ways of arranging them around a circular path such that 4 particular persons which include 2 particular men and 2 particular women never stand together is:

The number of integral solutions of \[ x+y+z=13 \] such that \[ 1\le x\le9,\qquad 0\le y\le9,\qquad 0\le z\le9 \] is

If \(\dfrac{{}^{\,n-1}C_{r-1}}{{}^{\,n}C_r}=\dfrac{3}{5}\) and \(\dfrac{{}^{\,n+1}C_{r+1}}{{}^{\,n}C_r}=\dfrac{11}{7}\), then \({}^{\,n}C_{r+3}\div{}^{\,r}C_{n/2}\) is equal to:

All the letters of the word REMAIN are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order. The rank of the word REMAIN, when counted from the rank of the word MARINE beginning with $1$ itself, is

In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is

Let $P$ and $Q$ are two sets such that \[ n(P)=27,\quad n(Q)=17,\quad n(P\cap Q)=5. \] If $x$ is the number of ways of selecting $7$ elements from $P$ such that all the elements of $P\cap Q$ are in each selection and $y$ is the number of ways of selecting $10$ elements from $Q$ such that no element of $P\cap Q$ is present in any selection, then $x+y+1=$

Committee of 5 from 5 Indians, 4 Americans, 3 Australians with at least one from each and max 2 per country.

Compute $p$ and $q$ ratio for circular + linear arrangements with constraints.

Number of 5-digit numbers using digits 3–9 with repetition, divisible by 7.

A student found 6 Mathematics books, 5 Physics books and 4 Chemistry books. If he buys at least one book of each subject, total number of ways is

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

The rank of the word ‘NEEDED’, when all letters of this word are permuted in all possible ways to form different 6-letter words and arranged in dictionary order, is

The number of skew symmetric matrices of order \( 3 \times 3 \) that can be formed by using all the elements 0, \( \pm a, \pm b, \pm c \) is:

Let the numerical values of the coefficients of a polynomial belong to the set \( \{0, 1, 2, \dots, 9\} \). Then the number of reciprocal polynomials of third degree with the leading coefficient 1 that can be formed is: