Combinations practice · Easy

In a network of railways, a small island has 15 stations. The number of different types of tickets to be printed for each class, if every station must have tickets for other station, are

There are two urns. Urn $A$ has 3 distinct red balls and urn $B$ has 9 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

If ${\;^8}{C_r} - {\;^7}{C_3} = {\;^7}{C_2}$, then $r$ is equal to

5-digit numbers are formed using 2, 3, 5, 7, 9 without repeating the digits. If $p$ is the number of such numbers that exceeds 20000 and $q$ be the number of those that lie between 30000 and 90000 then $p : q$ is:

A binary sequence is an array of 0's and 1's. The number of $n -$ digit binary sequence which contain even number of 0's is

The number of diagonals in a polygon of $m$ sides is

If in a chess tournament each contestant plays once against each of the other and in all 45 games are played, then the number of participants is

The number of positive integers satisfying the inequality ${ }^{n+1} C_{n-2}-{ }^{n+1} C_{n-1} \leq 100$ is

The maximum of points in to which 4 circles and 4 straight lines intersect is

The greatest possible number of points of intersection of 8 straight lines and 4 circle is

The number of ways in which 20 letters $x_1, x_2, … x_{10}, y_1, y_2, …, y_{10}$ be arranged in a line so that suffixes of the letters $x$ and also those of $y$ are respectively in ascending order of magnitude is

${\;^n}{C_r} + 2{\;^n}{C_{r - 1}} + {\;^n}{C_{r - 2}}$ is equal to

The number of positive odd divisors of 216 is

If ${}^n{C_4},{}^n{C_5},\mathrm{ }\,\,\mathrm{and }\,\,{}^n{C_6}$ are in AP, then n can be

From 12 books, the difference between number of ways a selection of 5 books when one specified book is always excluded and one specified book is always included, is

If ${\;^{35}}{C_{n + 7}} = {\;^{35}}{C_{4\;n - 2}}$, then all the values of $n$ are given by

The number of ways in which two teams $A$ and $B$ of 11 players each can be made up from 22 players so that two particular players are on the opposite sides is

The interior angles of a regular polygon measure ${160^0}$ each. The number of diagonals of the polygon are

The number of integral points on the hyperbola $x^{2}-y^{2}=(2000)^{2}$ is (an integral point is a point both of whose co-ordinates are integer)

The straight lines ${I_1},{I_2},{I_3}$ are parallel and lie in the same plane. A total numbers of $m$ points are taken on ${I_1},n$ points on ${I_2},k$ points on ${I_3}$. The maximum number of triangles formed with vertices at these points is

The number of times the digit 3 will be written when listing the integers from 1 to 1000 , is

A class consists of 4 boys and $g$ girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of $g$ is

Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done, if the group is to have a majority of boys?

The number of group that can be made from5 different green balls, 4 different blue balls and 3 different red balls, if at latest 1 green and 1 blue ball is to be included, is

Sita has 5 coins each of the different denomination. The number different sums of money she can form is

A person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite at a time, is

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

${\;^n}{C_r} + 2{\;^n}{C_{r - 1}} + {\;^n}{C_{r - 2}}$ is equal to

Number of diagonals of a polygon are 65 , then the number of sides of polygon are

The value of ${ }^{50} C_{4}+\sum_{r=1}^{6}{ }^{56-r} C_{3}$ is