Permutation and combination practice · Medium

The sum of all that can be formed with the digits 2,3,4,5 taken all at a time is

The number of distinct rational numbers $x$ such that $0 < x < 1$ and $x=\frac{p}{q}$, where $p, q \in\{1,2,3,4,5,6\}$ is

A class has $n$ students. We have to form a team of the students including atleast two students and also excluding atleast two students. The number of ways of forming the team is

The total number of flags with three horizontal strips, in order that can be formed using 2 identical red, 2 identical green and 2 identical white strips, is equal to

Letter of the word 'WATER' is arranged in all possible ways and written as dictionary then rank of the word 'WATER' is

A boat is to be managed by eight men of whom 2 can only row on bow side and 3 can only row on stroke side, the number of ways in which the crew can be arranged, is

Five digit number divisible by 3 is formed using $0,1,2,3,4$, 6 and 7 without repetition. Total number of such numbers are

The sum of all four digit numbers that can be med using the digits $1,2,3,4$, when repetition of digits is not allowed, is

The value of $\frac{(2 n) !}{n !}$ is

An $n$-digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of $n$ for which this is possible, is

Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain $n$ people, where $n$ is

The number of arrangements that can be formed out of GANESHPURI so that "The vowels are always together is

The number of integers, greater than 7000 that can
be formed, using the digits 3, 5, 6, 7, 8 without
repetition, is

If $n=2^{100} 3^2$ and $\left\{d_1, d_2, \ldots d_k\right\}$ is the set of all divisors of $n$, then $\sum\limits_{{j=1}}^k \frac{1}{d_j}$ equals

The total number of four-digit numbers having all different digits is equal to

If $n=2^{p-1}\left(2^p-1\right)$, where $2^p-1$ is a prime, then the sum of the divisors of $n$ is equal to

Two players $P_1$ and $P_2$ play a series of '$2 n$' games. Each game can result in either a win or loss for $P_1$. Total number of ways in which $P_1$ can win the series of these games, is equal to

15 identical balls have to be put in 5 different boxes. Each box can contain any number of balls. Total number of ways of putting the balls into box, so that each box contains atleast 2 balls, is equal to

number of ways in which 15 indistinguishable oranges can be distributed in 3 different boxes so that every has atmost 8 oranges is

Total number of 6 digit numbers in which all the odd digits and only odd digits appear is

The number of ordered pairs $(m, n)$, $m, n \in\{1,2, \ldots, 100\}$ such that $7^m+7^n$ is divisible by 5, is

The number of word formed by using all letter of word 'RANDOM' in which vowels are in alphabetical order is

In a single correct match the column question, column I contain 10 questions and Column II contain 10 answers written in some arbitrary order. If the number ways a student can answer this question so that exactly 6 of his matching are correct is $\mathrm{k}$, then (sum of digits of k) $/ 2$ is equal to

Let a be a factor of 120 . Then the number of positive integral solutions of $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3=\mathrm{a}$ is $\mathrm{k}$ then $\frac{\mathrm{k}}{80}$ is

The number of ways in which the sum of upper faces of four distinct dices can be six, is

The number of ways in which 3 children can distribute 10 tickets out of 15 consecutively numbered tickets themselves such that they get consecutive blocks of 5, 3 and 2 tickets is

In how many ways can 10 examination paper be arranged, so that the best and the worst papers never come together?

The number of natural numbers less than 1000, in which no two digits are replaced, is

No. of ways to give 16 different things to $A, B, C$ so that $B$ gets 1 more than $A$ and $C$ gets 2 more than $B$, is

The number of ways such that 6 persons can be selected from 4 officers and 8 constables, if at least one officer is to be included, is