Permutation and combination practice · Easy

Four boys picked 30 apples. The number of ways in which they can divide them if all the apples are identical, is

The total number of ways can 15 identical Mathematics books be distributed among six students, is

Three dice are rolled. The number of possible outcomes in which at least one die shows 5 is

When a group photograph is taken, all the seven teachers should be in the first row and all the twenty students should be in the second row. If the two corners of the second row are reserved for the two tallest students, interchangeable only between them, and if the middle seat of the front row is reserved for the principal. The no. of such possible 'arrangements' is

In a plane, there are two sets of parallel lines, one of $m$ lines and the other of $n$ lines. If the lines of one set cut those of the other, then the number of different parallelograms that can be formed is

$m$ men and $w$ women are to be seated in a row so that all women sit together. The number of ways in which they can be seated is

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text {th }}$ position in this arrangement is :

The number of natural numbers less than one million that can be formed by using the digits, 0, 2, and 3 is

There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is

If there are 62 onto mapping from a set $X$ containing $n$ elements to the set $Y=\{-1,1\}$, then $n$ is equal to:

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf, so that the dictionary is always in the middle. The number of such arrangements is

There are ' $n$ ' seats round a table numbered $1,2,3, \ldots n$ The numbers of in which $m(\leq n)$ persons can take seats is

The number of ways in which the letters of the word 'SUCCESSFUL' be arranged such that all the ' $s$ ' come together is

The number of ways in which 7 people can be arranged at a round table, so that 2 particular persons may be together, is

From 17 consonants and 5 vowels. The number of words containing 3 consonants and 2 vowels that can be made if all the letters are different, is

Let $x_1, x_2, x_3, \ldots, x_k$ be the divisors of positive integer ' $n$ ' (including 1 and $x$ ). If $x_1+x_2+\ldots+x_k=75$, then $\sum\limits_{i=1}^k \frac{1}{x_i}$ is equal to

A man invites 6 non-vegeterian and 5 vegeterian friends for a dinner party. He arrange 6 non-vegeterian friends on one round table and 5 vegeterian friends along another round table. The number of ways this can be done is:

The least positive integral value of $n$ which satisfies the inequality ${ }^{10} {C}_{n-1}>2 \cdot{ }^{10} {C}_n$ is

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

The rank of the word MOTHER when the letters of the word are arranged alphabetically as in a dictionary, is

A set contains $(2 n+1)$ elements. The number of subsets of the set which contain at most $n$ elements is

Let $A$ be the set of 4-digit numbers $a_1 a_2 a_3 a_4$, where $a_1 > a_2 > a_3 > a_4$, then $n(A)$ is equal to

How many numbers lying between 999 and 10000 can be formed with the help of the digits 0, 2, 3, 6, 7, 8 when the digits are not be repeated?

If each of 10 points on a straight line be joined to each of 10 points on a parallel line then the total number of triangles that can be formed with the given points as vertices, is

The value of ${ }^{50} C_4+\sum\limits_{{r=1}}^6{ }^{56-r} C_3$ is

Number of 4 digit numbers of the form $N=a b c d$ which satisfy following three conditions:

(i) $4000 \leq N < 6000$

(ii) $N$ is a multiple of 5

(iii) $3 \leq b < c \leq 6$

is equal to:

There are $n$ different books and $p$ copies of each. The number of ways in which a selection can be made from them is

If $x \in {N}$ and $\frac{(x+2) !}{(2 x-1) !} \cdot \frac{(2 x+1) !}{(x+3) !}=\frac{72}{7}$, then $x$ is equal to

The number of natural numbers smaller than ${10^4},$ in the decimal notation of which all the digit are different is

There are $p$ copies each of $n$ different books. The number of different ways in which a non-empty selection can be made from them, is