Permutation and combination practice · Medium

The number of natural numbers which are less than $2 \cdot 10^8$ and which can be written by means of the digit 1 and 2, is

If ${ }^{2 n+1} P_{n-1}:{ }^{2 n-1} P_n=3: 5$, then $n$ is equal to

There are 20 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions, then the maximum number of students who appeared in the examination, is

The total number of ways of arranging the letters AAAA BBB CC D E F in a row such that letters C are separated from one another is

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is

Sixteen men compete with one another in running swimming and riding. How many prize lists could be made if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?

A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions, so that exactly 10 predictions are correct, is equal to

Number of ways is which 50 identical books can be distributed in 100 students if each student can get atmost one book is

The number of words of four letters containing equal number of vowels and consonants, repetition allowed, is

The number of words which can be formed the letters of the word MAXIMUM, if two consonants cannot occur together, is

A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to

We are to form different words with the letters of the word INTEGER. Let ${m_1}$ be the number of words in which I and N are never together and ${m_2}$ be the number of words which begin with I and end with R, then ${m_1}/{m_2}$ is equal to

If ${ }^{56} P_{r+6}:{ }^{54} P_{r+3}=30800: 1$, then the value of $r$ is

The sum of the digits in the unit place of all the numbers formed with the help of $3,4,5,6$ taken all at a time is

Number of numbers greater than 24000 that can be formed by using $1,2,3,4,5$ when no digit being repeated is

Let $\mathrm{A}$ be the set of all positive prime integers less than 30 . The number of different rational numbers whose numerator and denominator belongs to $\mathrm{A}$ is

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , isThe number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is

$n$ different toys have to be distributed among $n$ children. Total number of ways in which these toys can be distributed, so that exactly one child gets no toy, is equal to

If letters of the word 'KUBER' are written in all possible orders and arranged as in a dictionary, then rank of the word 'KUBER' will be

The one's and ten's digits in $1 !+2 !+3 !+\ldots+49$! are respectively

The no. of ways in which 5 boys and 4 girls sit around a circular table so that no two girls sit together is

8 players $\mathrm{S}_1, \mathrm{~S}_2, \ldots . . . \mathrm{S}_8$, play in tournament. Number of ways in which they can be grouped into 4 pairs so that $S_1$ and $S_2$ are in different group is

Total no. of ways in which six ' + ' and four '-' signs can be arranged in a row so that no two '-' signs to be together, is

The number of ways 6 different flowers can be given to 10 girls, if each can receive any number of flowers is

The value of $\sum\limits_{{r=1}}^{15} r^2\left(\frac{{ }^{15} C_r}{{ }^{15} C_{r-1}}\right)$ is equal to:

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is $(6 !) k$, then $k$ is equal to

The number of 5-digit numbers that can be made using the digits 1 and 2 and in which atleast one digit is different, is

$\frac{(2 n) !}{2^{2 n}(n !)^2} \leq$

${\;^n}{P_r} = 3024$ and ${\;^n}{C_r} = 126$, then $r$ is

Find the number of permutations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ of numbers $1,2,3,4,5$ such that the sum of five products $x_{1} x_{2} x_{3}+x_{2} x_{3} x_{4}+x_{3} x_{4} x_{5}+x_{4} x_{5} x_{1}+x_{5} x_{1} x_{2}$ is divisible by 3