Permutation and combination practice · Easy

The sum of all 3- digited numbers that are divisible by either 3 or 4 but not by 48 is

The figure 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is

Find the remainder when $1 !+2 !+3 !+\ldots+n$! is divided by 15, if $n \geq 5$.

No.of ways of seating 20 persons at two round tables. Seating 10 to each table is

Number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

The number of words that can be formed out of the letters of the words ‘ARTICE’ so that the vowels occupy even places, is

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

The number of arrangements which can be made using all the letters of the word LAUGH, if the vowels are adjacent, is

The number of ways in which the letters of 'ARRANGE' be arranged so that "Two R's come together but Two A's do not come together is

The total number of three-digit numbers, the sum of whose digits is even, is equal to

If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated, is

The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between two boys is

The number of different words that can be formed from the letters of the word ‘PENCIL’ so that no two vowels are together, is

There are 10 persons among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers, is equal to

If there are 12 persons in a party, and if each of them shakes hands with each other, then number of handshakes happen in the party is

The number of words that can be formed from the letters of the word DAUGHTER so that the vowels always come together, is

The sum of all the four-digit numbers that can be formed using all the digits $2,1,2,3$ is equal to____

The number of ways of painting the faces of a cube with six different colours is

The number of ways in which the letters of the word 'SUCCESSFUL' be arranged such that no two S's will come together is

${X}$ has four friends ${A}, {B}, {C}, {D}$ he wants to invite one or more of them at dinner. If the invited persons(s) $\& \,X$ are sitting around a circular table then the arrangement in which $C\,\&\,D$ (if both are invited) are sitting together is

The total number of functions ' $f$ ' from the set $\{1,2,3\}$ into the set $\{1,2,3,4,5\}$ such that $f(i) \leqslant f(j),\forall i < j$, is

Let $a$ be a factor of 120, then the number of positive integral solutions of $x_1 x_2 x_3=a$ is

The sum $1\left( {1!} \right) + 2\left( {2\;!} \right) + 3\left( {3!} \right) + ... + n\left( {n!} \right)$ equal to

In a group of boys, two boys are brothers and in this group, 6 more boys are there. In how many ways, they can sit if the brothers are not to sit alongwith each other :

A library has a copies of one book, $b$ copies of each of two books, $c$ copies of each of three books and single copies of d books. The total number of ways in which these book can be distributed, is

Let $S_n=\sum\limits_{{r=1}}^n r!$. If $T_n=S_n-7\left[\frac{S_n}{7}\right]$, where $[x]$ denotes greatest integer $\leq x$, then $T_{100}$ is equal to

If $\mathrm{k}$ be the number of 3 digit natural numbers, having sum of their digits at least 10 , then find $\frac{k-35}{100}$.

If ${\;^{2n + 1}}{P_{n - 1}}:{\;^{2n - 1}}{P_n}:3:5$, then the value of $n$ is equal to

If ${ }^{15} C_{{r}+1}:{ }^{15} C_{3 {r}}=3: 11$, then value of $r$ is:

There are 10 points in a plane, of which no 3 points are collinear and 4 points are concyclic. The number of different circles that can be drawn through atleast 3 of these points, is