Permutation and combination practice · Easy

The number of even proper divisors of 1008 is

From 3 mangoes, 4 apples and 2 oranges. The number of selections of fruits that can be made, taking at least one of each kind is

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

The number of 3 letters words, with or without meaning which can be formed out of the letters of the word 'NUMBER'.

Statement I: When repetition of letters is not allowed is 120.

Statement II: When repetition of letters is allowed is 216.

Choose the correct option.

We are required to form different words with the help of 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 $\frac{m_1}{m_2}$ is given by

The number of five digit numbers that can be formed by using digits 1, 2, 3 only, such that three digits of the formed number are identical, is

The number of words that can be formed from the letters $a, b, c, d, e, f$, taken 3 at a time, each word containing at least one vowel is

The range of the function $f(x) = {}^{7-x} P_{x-3}$ is

The number of divisors of $n=2^7 \cdot 3^5 \cdot 5^3$, which are of the form $4 t+1(t \in N)$, is

$\sum \limits_{r = 0}^m {\;^{n + r}}{C_n}$ is equal to

The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is

The number of arrangements of the letters of the word "pencil" so that $e$ always comes earlier than $i$, is

Out of 5 apples, 10 mangoes and 15 oranges, the number of ways of distributing 15 fruits each to two persons, is $\mathrm{n}$ then $\frac{\mathrm{n}}{22}$ is equal to

Let $f:\left\{ {1,\;2,\;3,\;4,\;5} \right\} \to \left\{ {1,\;2,\;3,\;4,\;4,\;5} \right\}$ that are onto and $f\left( x \right) \ne i$ is equal to

The number of numbers lying between 40000 and 70000 that can be made from the digits $0,1,2,4,5,7$, if digits can be repeated in the same number, is

How many four-digit numbers can be formed using the digits $0,1,2,3,4,5$, if repetition of digits is not allowed?

All letters of the word EAMCET are arranged in all possible ways. The number of such arrangement in which no two vowels are adjacent to each other, is

In a certain test, $a_i$ students gave wrong answers to atleast $i$ questions, where $i=1,2,3, \ldots, k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is

Find the number of different necklaces that can be made from 17 identical pearls and 2 different diamonds.

Let $S=\{1,2,3, \ldots, n\}$. If $X$ denotes the set of all subsets of $S$ containing exactly two elements, then the value of $\sum\limits_{{A \in X}}(\min A)$ is

Five distinct letters are to be transmitted through a communication channel. A total number of 15 blanks is to be inserted between the two letters with at least three between every two. The number of ways in which this can be done is $t$ then $\frac{t}{400}$ is.

The sum of factors of $8 !$ which are odd and are of the form $3 m+2$, where $m$ is a natural number, is

The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MODESTY is

The number of ways in which two 10 paise, two 20 paise, three 25 paise and one 50 paise coins can be distributed among 8 children, so that each child gets only one coin, is

If ${ }^{n+5} p_{n+1}=\frac{1}{2}(11)(n-1)\left({ }^{n+3} p_n\right)$ then $n$ is equal to:

The number of arrangements that can be formed out of GANESHPURI so that "The vowels occupy even places are

In the decimal system of numeration, the number of 6-digit numbers in which the sum of digits is divisible by 5, is

How many numbers between 5000 and 10,000 can be formed using the digits 1,2,3,4,5,6,7,8,9, each digit appearing not more than once in each number?

The number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is

The numbers of times the digits 3 will be written when listing the integers from 1 to 1000 is