Permutations & Combinations Questions - JEE

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is

How many different committees of 5 members can be formed from 6 men and 4 ladies if each committee is to contain at least one lady?

The number of different ways to divide a set P of $n$ elements into two nonempty disjoint subsets whose union is P, is

In how many ways can we get a sum of at most 17 by throwing six distinct dice? In how many ways can we get a sum greater than 17?

In how many ways can a team of 11 players be formed out of 25 players, if 6 out of them are always to be included and 5 always to be excluded?

There are two possible combinations (1 Boy + 2 Girls) or (2 Boys + 1 Girl). The number of ways ${}^5C_1 \cdot {}^nC_2 + {}^5C_2 \cdot {}^nC_1 = 1750$.That is, $\left(5 \times \dfrac{n(n-1)}{2 \times 1}\right) + \left(\dfrac{5 \times 4}{2} \times n\right) = 1750$Find the value of $n$.

Match the following lists and choose the correct code.List IList IIa. Four dice (six faced) are rolled. The number of possible outcomes in which at least one dice shows 2 isp. 210b. Let $A$ be the set of 4-digit number $a_1 a_2 a_3 a_4$, where $a_1 > a_2 > a_3 > a_4$. Then $n(A)$ is equal toq. 480c. The total number of three-digit numbers, the sum of whose digits is even, is equal tor. 671d. The number of four-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 iss. 450Codes:abcd(1)qspr(2)srqp(3)rpsq(4)psqr

Find the number of pairs of parallel diagonals in a regular polygon of 10 sides.

A delegation of four students is to be selected from a total of 12 students. In how many ways can the delegation be selected in each of the following cases?(i) if all the students are equally willing?(ii) if two particular students have to be included in the delegation?(iii) if two particular students do not wish to be together in the delegation?(iv) if two particular students wish to be included together only in the delegation?(v) if two particular students refuse to be together and two other particular students wish to be together only in the delegation?

Three friends went to a shopping mall with $ 6, 7 and 8 with them in how many ways they can pay a bill of $ 10 if they have note of only one denomination.

If the 11 letters $A, B, \ldots, K$ denote an arbitrary permutation of the integers $(1, 2, \ldots, 11)$, then $(A-1)(B-2)(C-3)\cdots(K-11)$ will be

If the total number of strictly increasing functions defined from $f : \{1,2,3,4,5,6\} \to \{1,2,3,...,9\}$ is $k$ then $\frac{k}{12}$ is equal to _______

Given ${}^nC_4$, ${}^nC_5$ and ${}^nC_6$ are in A.P., then $2\cdot{}^nC_5 = {}^nC_4 + {}^nC_6$. Find the value of $n$ (take the larger value).

Let 52 cards of a deck be arranged in a line. Number of ways in which red cards appear in non-decreasing order of denomination is

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to

Consider a set $S = \{1, 2, \ldots, 100\}$ two elements $p$ and $q$ are selected from this set $S$ such that $7^p + 7^q$ is divisible by 5. How many ways this selection can be made?

Number of non-empty subsets of $\{1, 2, 3, \ldots, 12\}$ having the property that sum of the largest and smallest element is 13.

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is __________.

The number of ways the novels can be arranged is$x = {}^6C_4 \times {}^3C_1 \times 4!$What is the value of $x$?

$A_1A_2.......A_{2n}$ is regular $2n$ sided polygon $(n \geq 3)$. Find the ratio of number of obtuse angled triangles to the number of acute angled triangles formed by joining the vertices of the polygon.

Ten guests are to be seated in a row of which three are ladies. The ladies insist on sitting together while two of the gentlemen refuse to take consecutive seats. In how many ways can the guests be seated?

In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together?

Find the number of integral solutions of $x_1 + x_2 + x_3 = 24$ subjected to the condition that $1 \leq x_1 \leq 5$, $12 \leq x_2 \leq 18$ and $-1 \leq x_3$.

The total number of integral solution for $x, y, z$ such that $xyz=24$ is:

Statement 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^9C_3$.Statement 2: The number of ways of choosing any 3 places from 9 different places is $^9C_3$.(1) Statement 1 is false, statement 2 is true.

20 persons are sitting in a particular arrangement around a circular table. Three persons are to be selected for leaders. The number of ways of selection of three persons such that no two were sitting adjacent to each other is

In a class tournament, all participants were to play different games with one another. Two players fell ill after having played three games each. If the total number of games played in the tournament is equal to 84, the total number of participants in the beginning was equal to

A condolence meeting is being held in a big hall which has 7 doors by which the mourners enter the hall. One can use any one of the 7 doors to enter and can come at anytime during the meeting. At each door a register is kept in which a mourner has to put down his signature while entering the hall. If 200 people attend the meeting, how many different sets of 7 lists of signatures can arise?

To find the position of the word QUEEN in the dictionary arrangement of its letters, what position does QUEEN occupy?

How many words can be formed using all the letters of the word ASSASSINATION?

Let A = {1, 2, 3, 4, 5}. Find the total number of functions f : A → A such that f(f(x)) = x for all x ∈ A (i.e., involutions on A). The answer is 26.

If all the words formed from the letters of the word HORROR are arranged in the opposite order as they are in a dictionary, then the rank of the word HORROR is

Each of 5 women who attend a banquet checks her coat and hat with the receptionist on arrival. Upon leaving, each woman is given a coat and a hat at random. Find the number of ways these coats and hats may be distributed such that nobody gets back both her coat and her hat.

If m parallel lines in a plane are intersected by a family of n other parallel lines, then find the total number of parallelograms formed.

A six digit number which does not satisfy the property mentioned above (for each digit, not more than two digits smaller than that digit appear to the right of that digit), is:

If a vowel appears in between two similar letters, the number of simple words is

The number of words of four letters that can be formed from the letters of the word EXAMINATION is

The value of $({}^{21}C_1 - {}^{10}C_1) + ({}^{21}C_2 - {}^{10}C_2) + ({}^{21}C_3 - {}^{10}C_3) + ({}^{21}C_4 - {}^{10}C_4) + \cdots + ({}^{21}C_{10} - {}^{10}C_{10})$ is

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is

To form a committee of 11 persons from 8 male candidates and 5 female candidates, the number of ways $m$ to form a committee with at least 6 males equals the number of ways $n$ to form a committee with at least 3 females. What is the value of $m = n$?

Number of 7 letter dull words in which no two vowels are together, is

Number of six digit numbers that can be formed using digits 1, 2, 3, 4, 5, 6 (each digit used exactly once) having the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit, is:

Find the total number of 9-digit numbers which have all different digits.

Let $N$ be the number of four digit even numbers such that if 3 is one of the digits, then 5 is the succeeding digit. If $N = P_1^\alpha P_2^\beta P_3^\gamma$ ($P_1,P_2,P_3$ are primes, $\alpha,\beta,\gamma\in\mathbb{N}$), then $P_1+P_2+P_3$ is

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is

If the ratio ${}^{2n}C_3 : {}^nC_3$ is equal to 11:1, find n.

The value of ${}^{50}C_4 + \displaystyle\sum_{r=1}^{6} {}^{56-r}C_3$ is

Let $n$ be the number of sides of a regular polygon. If the number of diagonals of the polygon is 54, then the number of sides $n$ is:

Find the value of r, if $^{22}P_{r+1} : \,^{20}P_{r+2} = 11 : 52$

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then find the number of ways in which they can be seated.

Permutations & Combinations Questions (855)