Permutation and combination practice · Mixed difficulty

Ten persons, amongst whom are $A,B$ and $C$ to speak at a function. The number of ways in which it can be done, if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is

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

How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is not allowed)?

In how many ways vertices of a square can be coloured with $\mathbf{4}$ distinct colour if rotations are considered to be equivalent, but reflections are distinct?

How many arrangements can be made out of the letters of the word &quot; MOTHER&quot; taken four at a time so that each arrangement contains the letter &#39; $\mathrm{M}^{\text {'? }}$

The value of $\sum\limits_{{r=1}}^n \frac{{ }^n P_r}{r !}$ is

There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given, is

The number of other ways in which the letters of the work SIMPLETON can be rearranged is

The number of quadratic expression with the coefficients drawn from set $\{0,1,2,3\}$ is

The number of times the digit 5 will be written when listing the integers from 1 to 1000, is

Assuming that no two consecutive digits are same. The number of n digit numbers is

Let ${n} \in N$ satisfy ${ }^{2 {n}+1} {P}_{{n}-1} /{ }^{{2n}+1} {P}_{{n}}=\frac{3}{5}$ then equals to

The ten’s digit in $1! + 4! + 7! + 10! + 12! + 13! + 15! + 16! + 17!$ is divisible by

Let $R=\{a, b, c, d\}$ and $S=\{1,2,3\}$, then the number of functions $f$, from $R$ to $S$, which are onto is

In how many ways can 15 members of a council sit along a circular table, when the Secretary is to sit on one side of the chairman and the Deputy Secretary on the other side?

A total number of wards which can be formed out the letters $a,\;b,\;c,\;d,\;e,\;f$ taken 3 together such that each word contains at least one vowel, is

In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together?

The number of ways in which one can post 5 letters in 7 letters boxes is

The total number of arrangements which can be made out of the letters of the word ‘Algebra’, without altering the relative position of vowels and consonants is

From 4 gentlemen and 6 ladies, a committee of five is to be selected. The number of ways, in which the committee can be formed so that gentlemen are in majority, is

If $P_r$ stands for ${ }^r P_r$, then sum of the series $1+P_1+2 P_2+3 P_3+\ldots+n P_n$ is

The number of positive integral solutions of $x+y+z=n, n \in N, n \geq 3$ is

In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct, is

The Chief Minister of 11 states of India meet to discuss the language problem. The number of ways they can seat themselves at a round table so that Punjab and Chennai Chief Ministers sit together, is

If $(n+1) !=12 \times(n-1)$!, then $n$ is equal to

How many numbers greater than 24000 can be formed by using the digits 1,2,3,4,5 when no digit is repeated , is

The letters of the word 'RANDOM' are arranged in all possible ways. The number of arrangements in which there are 2 letters between $\mathrm{R}$ and $\mathrm{D}$ is

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0,1,3,5,7$ and 9 without repetition, is equal to

The number of ways in which $n$ books can be arranged on a shelf so that two particular books shall not be together is

The number of words from the letters of the word 'BHARAT' in which $\mathrm{B}$ and $\mathrm{H}$ never come together is