Permutations & Combinations Questions - JEE

In an election three districts are to be canvassed by 2, 3 and 5 men respectively. If 10 men volunteer, the number of ways they can be allotted to the different districts is:

If all the permutations of the letters in the word OBJECT are arranged (and numbered serially) in alphabetical order as in a dictionary, then the 717th word is

In an Ice cream parlor at South City Mall Kolkata, 4 different varieties of ice creams namely Vanila, Strawberry, Chocolate and Butter Scotch were available. On a particular day it was noticed that each customer bought at least one ice cream and at max 10 ice creams, on further investigation it was noticed that no two customer bought same set of ice creams then if the number of customers visited the ice cream shop on that particular day is $k$ then $\frac{k}{100}$ is ______.

Mr. Anshuman has thrown a dice 6 times in $k$ ways we can get a sum greater than 17 then $\frac{k}{10000}$ is_____.

Number of ways in which 9 different toys be distributed among 4 children belonging to different age groups in such a way that distribution among the 3 elder children is even and the youngest one is to receive one toy more, is:

If $k$ is the number of positive integral solutions of the in equality $a+b+3c \leq 30$ ? Then $\frac{k}{5}$ is_____.

Each set has $m$ parallel lines. If the total number of parallelograms thus formed is 225 then $m$ is equal to_____.

The total number of ways in which 10 Men and 10 Women can form 10 mixed complex (a mixed couple contain a Man and a Woman) is $N$, then $\frac{N}{9!}$ is equal to_____.

'A' is a set containing 'n' different elements. A subset P of 'A' is chosen. The set 'A' is reconstructed by replacing the elements of P. A subset 'Q' of 'A' is again chosen. The number of ways of choosing P and Q so that $P \cap Q$ contains exactly two elements is

Consider 5 points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or coincident. From each point perpendiculars are drawn to all the lines joining the other four points. Determine the maximum number of intersections that these perpendiculars can have?

Consider a set $X = \{1, 2, 3, \ldots, 9, 10\}$. If the number of pairs $[A, B]$ such that $A \subseteq X$ and $B \subseteq X$ also $A \neq B$ and $A \cap B = \{2, 3, 5, 7\}$ is $3\lambda - 4$ then $\lambda - \mu$ is_____.

Number of four-digit number between 5000 and 6000 such that the thousand’s digit is equal to the sum of the other three-digit, is:

In a particular batch of VIDYAMANDIR CLASSES Boston, there are 4 boys and certain number of girls. In every mock test only 5 students including at least 3 boys can appear. If different group of students write the Mock exam every time and number of times test conducted is 66 then find the total number of students in the class.

Find the minimum value of $k$ such that $(k!)$ is completely divisible by all two-digit prime numbers.

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to

There are counters available in $3$ different colours (atleast four of each colour). Counters are all alike except for the colour. If '$m$' denotes the number of arrangements of four counters if no arrangement consists of counters of same colour and '$n$' denotes the corresponding figure when every arrangement consists of counters of each colour, then:

How many sides are there in a polygon which has 35 diagonals?

Three digit numbers in which the middle one is a perfect square are formed using the digits $1$ to $9$. Their sum is:

Number of selections of 6 different letters can be made from the words NISHIT and RAHUL so that each selection consists of 3 letters from each word, is:

In the identity $\displaystyle\sum_{k=0}^{n} \frac{A_k}{x+k} = \frac{n!}{x(x+1)(x+2)\cdots(x+n)}$, the value of $A_i$ is

Find the number of ways in which 13 identical apples can be distributed among 3 persons so that no two persons receive equal number of apples and each can receive any number of apples.

With 17 consonants and 5 vowels, the number of four-letter words that can be formed having 2 vowels in the middle and one consonant repeated or different consonants at each end is

Number of ways in which the letters of the word "NATION" can be filled in the given figure such that no row remains empty and each box contains not more than one letter, are:

3 girls and 4 boys (including $B_1$ and $B_2$) stand in a queue. The number of arrangements where all girls stand together and all boys stand together, but $B_1$ and $B_2$ are not adjacent, is

Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If $T_{n-1} - T_n = 21$, then n equals

There are two urns. Urn $A$ has three distinct red balls and urn $B$ has nine distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Find the number of ways in which 8 different flowers can be strung to form a garland so that four particular flowers are never separated.

The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is

An $n$-digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$-digit numbers are to be formed using only the three digits 2, 5 and 7. Find the smallest value of $n$ for which this is possible.

Find the maximum number of points of intersection of 6 circles.

Number of functions defined from $f:{\{1,2,3,4,5,6\} \to \{7,8,9,10\}}$ such that the sum $f(1)+f(2)+f(3)+f(4)+f(5)+f(6)$ is odd, is:

In how many ways can 14 identical toys be distributed among three boys so that each one gets at least one toy and no two boys get equal number of toys?

Number of ways in which a lawn-tennis mixed double be made from seven married couples if no husband and wife play in the same set is

A telegraph has a number of arms and each arm is capable of taking 4 distinct positions, including the position of rest. If 1023 different signals can be sent in all then find the number of arms.

Let $0\leq r\leq n$. If $^{n+1}C_{r+1}:^nC_r:^{n-1}C_{r-1}=55:35:21$, then $2n+5r$ is equal to:

Let $P$ be the set of all 7-digit numbers that can be formed using only the digits 1, 2, 3 with digit sum equal to 11. Then $|P|$ equals

n different toys have to be distributed among n children. Total number of ways in which these toys can be distributed so that exactly one child gets no toy, is equal to

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

There are 5 mangoes and 4 apples. In how many different ways can a selection of fruits be made if fruits of the same kind are identical?

Sixteen players $S_1, S_2, S_3, \ldots, S_{16}$ play in a tournament. Number of ways in which they can be grouped into eight pairs so that $S_1$ and $S_2$ are in different pairs, is

In a class, there are 15 boys and 10 girls. How many ways a teacher can select 1 boy and 1 girl to represent the class at a seminar?

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is:

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is

If $P = 21(21^2 - 1^2)(21^2 - 2^2)(21^2 - 3^2) \cdots (21^2 - 10^2)$, then P is divisible by

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$ is ________.

The number of 6-letter words that can be formed using the letters of the word MATHS (M, A, T, H, S — all distinct), where every letter that appears in the word must appear at least twice, is

In how many ways can 17 persons depart from railway station in 2 cars and 3 autos, given that 2 particular persons depart by the same car (4 persons can sit in a car and 3 persons can sit in an auto)?

Find the number of odd proper divisors of $3^p \times 6^m \times 21^n$.

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

If ${}^nC_r = 84$, ${}^nC_{r-1} = 36$, and ${}^nC_{r+1} = 126$, then find the value of n.

Permutations & Combinations Questions (855)