Permutations and Combinations · Mathematics · AP EAPCET

$$\text { If } 10{ }^n C_2=3^{n+1} C_3 \text {, then the value of } n \text { is }$$

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

In an examination, the maximum marks for each of three subjects is $$n$$ and that for the fourth subject is $$2 n$$. The number of ways in which candidates can get $$3 n$$ marks is

If a set $$A$$ has $$m$$-elements and the set $$B$$ has $$n$$-elements, then the number of injections from $$A$$ to $$B$$ is

In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

A natural number $$n$$ such that $$n!$$ ends in exactly 1000 zeroes is

The total number of permutations of $$n$$ different things taken not more than $$r$$ at a time, when each thing may be repeated any number of times is

How many chords can be drawn through 21 points on a circle?

If a polygon of $$n$$ sides has 560 diagonals, then $$n=$$

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes? Notation $$D_n=n!\left(\sum_\limits{i=0}^n \frac{(-1)^i}{i!}\right)$$

The value of $${ }^6 P_4+4 \cdot{ }^6 P_3$$ is

The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is

In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?

For $$1 \leq r \leq n, \frac{1}{r+1}\left\{{ }^n P_{r+1}-{ }^{(n-1)} P_{r+1}\right\}$$ is equal to

In how many ways 4 balls can be picked from 6 black and 4 green coloured balls such that at least one black ball is selected?

In how many ways can 9 examination papers be arranged so, that the best and the worst papers are never together?

If a person has 3 coins of different denominations, the number of different sums can be formed is

There are 7 identical white balls and 3 identical black balls. The number of distinguishable arrangements in a row of all the balls, so that no two black balls are adjacent is

The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one ring is

If the letters of the word REGULATIONS be arranged in such a way that relative positions of the letters of the word GULATIONS remain the same, then the probability that there are exactly 4 letters between R and E is