Permutation and combination practice · Easy

In how many ways 3 letters can be posted in 4 letter-boxes, if all the letters are not posted in the same letter-box?

If the permutations of $a, b, c, d$ and $e$ taken all together are written down in alphabetical order as in dictionary and numbered, the rank of the permutation debac is

Find the number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated

If ${ }^{(m+n)} P_2=90$ and $^{(m-n)} P_2=30$, then $(m, n)$ is

If $0 < r < s \leq n$ and ${ }^n P_r={ }^n P_s$, then value of $r+s$ is

$\left({ }^8 {C}_1-{ }^8 {C}_2+{ }^8 {C}_3-{ }^8 {C}_4+{ }^8 {C}_5-{ }^8 {C}_6+{ }^8 {C}_7-{ }^8 {C}_8\right)$ equals:

If ${ }^n C_3+{ }^n C_4 > { }^{n+1} C_3$, then

The number of ways of putting 5 identical balls in 10 identical boxes, if not more than one can go in a box is

There are 10 true-false questions in an examination. Then, these questions can be answered in

The products of any $r$ consecutive natural numbers is always divisible by

The value of $\left( {{{2.}^1}{P_0} - {{3.}^2}{P_1} + {4^3}{P_2}......\mathrm{upto}{\mkern 1mu} {\mkern 1mu} \mathrm{51th}{\mkern 1mu} {\mkern 1mu} \mathrm{term}} \right)\mathrm{ + }\left( {\mathrm{1}! - \mathrm{2}!\mathrm{ + 3}!...\mathrm{upto}{\mkern 1mu} {\mkern 1mu} \mathrm{51th}{\mkern 1mu} {\mkern 1mu} \mathrm{term}} \right)$ is equal to

Four boys picked up 30 mangoes. The number of ways in which they can divide them if all mangoes be identical, is

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls, is

If ${ }^{{n}+2} C_3={ }^{{n}+3} P_2-20$, then $n$ is equal to:

The number of ways in which 3 boys and 3 girls (all are of different heights) can be arranged in a line, so that boys as well as girls among themselves are in decreasing order of height from left to right, is

Number of positive integer $n$ less than 17, for which $n !+(n+1) !+(n+2)!$ is an integral multiple of 49, is

If $l=\operatorname{LCM}$ of 8 !, 10 ! and 12 ! and $h=\operatorname{HCF}$ of 8 !, 10 ! and 12 !, then $\frac{l}{h}$ is equal to

The total number of factors (excluding 1) of 2160 is

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time, $b$ the number of permutations of $x$ things taken 11 at a time and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182\;bc$, then the value of $x$ is

Total number of positive integral solutions of $x_1 \cdot x_2 \cdot x_3=60$ is equal to

The number of bijective functions $f:\{1,3,5,7, \ldots$, $99\} \rightarrow\{2,4,6,8, \ldots \ldots, 100\}$ such that $f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \geq f(99)$, is _____.

An examination paper contains 8 question of which 4 has 3 possible answers, 3 have 2 possible answers each and the remaining one question has 5 possible answers. The total number of possible answers to all the questions is

There are three copies, each of 4 different books. The number of ways in which they can be arranged on a shelf, is

12 boys and 2 girls are to be seated in a row such that there are atleast 3 boys between the 2 girls. The number of ways this can be done is $\lambda \times 12 !$ ! the value of $\lambda$ is

The number of squares that we can find on a chess board is

The total number of proper factors of 7875 is

The number of positive terms in the sequence $x_n=\frac{195}{4{ }^n P_n}-\frac{{ }^{n+3} P_3}{{ }^{n+1} P_{n+1}}, n \in N$ is

The number of ways in which 5 boys and 5 girls can sit in a row so that all girls sit together is

The no. of dissimilar terms in the expansion of $(a+b+c)^{10}$ is

The total number of selections of at least one red ball from a bag containing 4 red balls and 3 green balls, balls of the same colour being identical, is