Permutation and combination practice · Mixed difficulty

The number of numbers between 2,000 and 5,000 that can be formed with the digits $0,1,2,3,4$, (repetition of digits is not allowed) and are multiple of 3 is?

An urn contains 3 red pens, 4 green pens and 6 yellow pens. The number of ways of drawing 4 pens from the urn, if atleast one red pen is to be included in the draw, is (all the pens are different from each other)

The number of functions $f$ from the set $A=\{0,1,2\}$ into the set $B=\{0,1,2,3,4,5,6,7\}$ such that $f(i) \leq f(j)$ for $i < j$ and $i, j \in A$, is

The letters of the word 'VICTORY' are arranged in all possible ways, and the words thus obtained are arranged as in a dictionary. Then the rank of given word is

If the words formed by using the letters of the word 'AGAIN' are arranged in the form of dictionary, then $50^{\text {th }}$ word is

How many words can be made from the letters of the word DELHI, if $L$ comes in the middle of every word?

Let $\mathrm{T}_4$ denotes the number of triangles which can be formed by using the vertices of a regular polygon of $n$ sides, If $T_{n+1}-T_n=21$, then $n$ equals.

From 5 consonants, 4 vowels and 3 capital letters, the number of words beginning with a capital letter and containing 3 consonants and 2 vowels that can be made is

The number of diagonals that can be drawn by joining the vertices of an octagon is

Find the number of chains that can be prepared using 5 different colored beads

There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is

$n$ lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut, is

5 different objects are to be distributed among 3 persons such that no two persons get the same number of objects. Number of ways this can be done, is

The number of ways by which letter of word ASSASSINATION can be arranged such that all vowels come together is:

In how many ways can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student?

A telegraph has 5 arms and each arm is capable of 4 distinct positions, including the position of rest. The total number of signals that can be made is

If all the words (with or without meaning having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

The number of rational numbers lying in the interval $(2002,2003)$ all whose digits after the decimal points are non-zero and are in decreasing order, is

The total number of words that can be formed using all letters of the word 'RITESH' that neither begins with I nor ends with $\mathrm{R}$, is

The number of ways in which 10 boys and 10 girls can be seated in a row so that boys and girls alternate is

How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?

Two straight lines intersect at a point $O$. Points $A_1, A_2, \ldots, A_n$ are taken on one line and points $B_1, B_2, \ldots, B_n$ on the other. If the point $O$ is not to be used, then the number of triangles that can be drawn using these points as vertices, is

The number of integral solutions of $x_1+x_2+x_3=0$, with $x_i \geq-5$, is

The number of ways of selecting 4 letters from the word EXAMINATION, is

The number of different pairs of words $(\square \square \square \square, \square \square \square)$ that can be made with the letters of the word 'STATICS' is

There are 5 boys and 3 girls. In how many ways can they be seated in a row, so that all the three girls do not sit together?

In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together?

The total number of six-digit numbers that can be formed, having the property that every succeeding digit is greater than the preceding digit, is

Value of $\frac{n !}{(n-r) !}$ when $n=6, r=2$ is $5{m}$. The value of $m$ is

The largest integer $n$ such that 33 ! is divisible by $2^n$ is