Combinations practice · Easy

If a polygon has 44 diagonals, then the number of its sides are

${ }^{14} {C}_7+\sum\limits_ {{i}=1}^3{ }^{17-{i}} {C}_6=$

Six points in a plane be joined in all possible ways by indefinite straight lines and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points or intersection is equal to

The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{5 ! 1 !}$ is :

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then, the number of such arrangements is

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is

The number of integers which lie between 1 and ${10^6}$ and which have the sum of the digits equal to 12, is

Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ${n_i},$ the label of the ball drawn from $i$ th box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that ${n_1} < {n_2} < {n_3}$ is

Find ${ }^n C_{21}$, if ${ }^n C_{10}={ }^n C_{11}$.

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

The results of 21 football matches (win, lose or draw) are to be predicted. The number of forecasts that contain exactly 18 correct results is

There are 10 points in a plane, out of these 6 are collinear. The number of triangles formed by joining these points is

The total number of different combinations of letters which can be made from the letters of the word MISSISSIPPI is

A person goes for an examination in which there are four papers with a maximum of m marks from each paper. The number of ways in which one can get $2m$ marks, is

If the number of ways of selecting $n$ cards out of unlimited number of cards bearing the number $0,9,3$, so that they cannot be used to write the number 903 is 93 , then $n$ is equal to

A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attent the party together, is

In a cricket championship there are 36 matches. The number of terms, if each plays 1 match with other are

At an election, a voter may vote for any number of candidates, not greater than number to be elected. There are 10 candidates and 4 are to be selected. If a voter votes for atleast one candidate, then number of ways in which he can vote, is

The number of ordered pairs of non-negative integers $\{x, y\}$ having sum 7596 without any carries is equal to

The number of diagonals of a polygon of 20 sides is

In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be 126, then the number of contestants is

At an electron, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is

Let $A$ be the set of 4 digit number ${a_1}{a_2}{a_3}{a_4},\;\mathrm{where}\;{a_1} < {a_2} < {a_3} < {a_4},$ then $n\left( A \right)$ is equal to

There are 10 points in a plane, out of these 6 are collinear. If $N$ is the number of triangles formed by joining these points, then

Given 6 different toys of green colour, 5 different toys of blue co- lour and 4 different toys of red colour. Combination of toys that can be chosen taking at least one green and one blue toys are

There are 5 points ${P}_1, {P}_2, {P}_3, {P}_4, {P}_5$ on the side ${AB}$, excluding $A$ and $B$, of a triangle $A B C$. Similarly there are 6 points ${P}_6, {P}_7, \ldots, {P}_{11}$ on the side ${BC}$ and 7 points ${P}_{12}, {P}_{13}, \ldots, {P}_{18}$ on the side ${CA}$ of the triangle. The number of triangles, that can be formed using the points ${P}_1, {P}_2, \ldots, {P}_{18}$ as vertices, is:

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

The number of diagonals in a octagon will be

If ${\;^n}{C_r} = {\;^n}{C_{r - 1}}{\text{\;and}}\;{\;^n}{P_r} = {\;^n}{P_{r + 1}}$, then the value of $n$ is

The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is