Permutation and combination practice · Mixed difficulty

If $f:\{1,2,3,4,5\} \rightarrow\{x, y, z, t\}$, then the total number of onto functions is equal to

Find the number of ways of arranging 6 boys and 6 girls around a circle

The number of different 7 digit numbers that can be written using only the three digits 1,2 and 3 with the condition that the digit 2 occurs twice in each number is

The number of ways in which 10 person can sit around a table so that they do not have same neighbor (all at once) in any two arrangements

The range of the function $f(x)={ }^{15-x} P_{x-8}$ is

Let $A$ be the set of four digit numbers $a_1 a_2 a_3 a_4$, where ${a_1} > {a_2} > {a_3} > {a_4}$, then $n(A)$ is

Let $E=\left[\frac{1}{3}+\frac{1}{50}\right]+\left[\frac{1}{3}+\frac{2}{50}\right]+\left[\frac{1}{3}+\frac{3}{50}\right]+\ldots+50 \text { terms,}$ then the exponent of 2 in $E$! is

The letters of the word "CONTINUE" are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangements is

Out of 10 consonants four vowels, the number of words that can be formed using six consonants and three vowels

The number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is

$S_n=1 !+2 !+3 !+4 !+\ldots+n !$ cannot be the square of natural number except for $n$, is

A meeting is to be addressed by 5 speakers A, B, C, D, E. In how many ways can the speakers be ordered, if $B$ must not precede A (immediately or otherwise)?

The number of non-negative integral solutions of $a+b+c+d=n, n \in N$, is

If $\frac{1}{6 !}+\frac{1}{7 !}=\frac{x}{8 !}$, then the value of $x=2^m$. The value of $m$ is

There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that two particular ladies refuse to sit beside a particular gentleman?

Let $S_n=\sum\limits_{{r=1}}^n r ! ; (n > 6)$, then $S_n-7\left[\frac{S_n}{7}\right]$ (where, [ ] denotes the greatest integer function) is equal to

The number of positive integers with the property that they can be expressed as the sum of the cubes of 2 positive integers in two different ways is

The value of ${\;^n}{P_r}$ is equal to

There are 5 different coloured balls and 5 boxes of the same colour as that of the balls. The number of ways that exactly 2 balls will go to the boxes of their own colour is

Find the number of ways of arranging the letters of the word 'PESSIMISTIC'

In a town the car plate numbers contains only three or four digits, not containing the digit 0. The
maximum number of cars that can be numbered is

In an examination, the maximum marks for each of three papers is $n$ and that for fourth paper is $2 n$. Then, the number of ways in which a candidate can get $3 n$ marks, is

Total number of divisors of $n=3^5 \cdot 5^7 \cdot 7^9$ that are of the form $4 \lambda+1, \lambda \geq 0$, is equal to

Among $9!$ permutations of the digits $1,2,3, \ldots, 9$. Consider those arrangements which have the property that if we take any five consecutive positions, the product of the digits in those positions is divisible by 7, the number of such arrangements is

Let $A$ denotes the property that two elements of $A=\{1,5,9,13, \ldots, 1093\}$ add upto 1094. Then, maximum number of elements in $A$ can be

A team of four students is to be selected from a total of 12 students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64 . The number of telephone numbers having all six digits distinct is

Three straight lines $l_1, l_2$ and $l_3$ are parallel and lie in the same plane. Five points are taken on each of $l_1$, $l_2$ and $l_3$. The maximum number of triangles which can be obtained with vertices at these points, is

The number of polynomials of the form $x^3+a x^2+b x+c$ that are divisible by $x^2+1$, where $a$, $b, c \in\{1,2,3,4,5,6,7,8,9,10\}$, is