Permutation and combination practice · Easy

The positive integer $r$, such that ${ }^{15} {C}_{3 r}={ }^{15} {C}_{r+3}$, is equal to

The number of numbers of 4 digits which are not divisible by 5, are

ABCD is a quadrilateral. $3,4,5$ and 6 points are marked on the sides $\mathrm{AB}, {BC}, {CD}$ and ${DA}$ respectively. The number of triangles with vertices on different sides is

Let $Q_{{n}}$ be the number of possible quadrilaterals formed by joining vertices of an $n$ sided regular polygon. If $Q_{n+1}-Q_n=20$, then value of $n$ is:

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed by joining them is

How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together?

The number of all possible selections of one or more questions from 10 given questions, each question having an alternative is

All possible four-digit numbers are formed using the digits 0,1,2,3 so that no number has repeated digits. The number of even number among them is

In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together?

The number of numbers lying in $(2,3)$, where all the digits after decimal are non-zero and in increasing order, is

If $33 !$ is divisible by $2^n$, then the maximum value of $n$ is equal to

12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is

The number of rectangles excluding squares from a rectangle of size $9 \times 6$ is

If eleven member of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is

The total numbers of greater than 100 and divisible by 5, that can be formed from the digits 3,4,5,6 if no digit is repeated is

From 4 Officers and 8 Jawans, a committee of 6 is to be chosen to include exactly one officer. The number of such committee is

The number of ways in which ten candidates $A_1, A_2, A_3, A_4, \cdots, A_{10}$ can be arranged in a row "If $A_1$ is always above $A_2$ is

There are three teams each of a chairman, a supervisor and a worker three different companies. There are nine bonus of different denominations to be paid to these nine persons in all. In how many ways can this be done with due respect to superiority is given in every team?

The number of possible outcomes in a throw of $n$ ordinary dice in which atleast one of the dice shows an odd number, is

In a class, there are 15 boys and 10 girls. The teacher wants to select a boy and a girl to represent the class in a function, then the total number of selection by teacher is

If there are $n$ number of seats and m number of people have to be seated, then how many ways are possible to do this $(m < n)$ ?

How many numbers between 400 and 1000 can be made with the digits 2, 3, 4, 5, 6 and 0?

Three alike red roses and three alike pink roses are used to form a garland. The number of ways is

How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice?

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is

The number of straight lines that can be drawn out of 10 points of which 7 are collinear

A letter lock consists of three rings each marked with 10 different letters. No. of ways to make an unsuccessful attempts to open the lock is

A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

There are $n$ number of sets and m number of people have to be seated, then how many ways are possible to do this $\left( {m < n} \right)?$