Permutation and combination practice · Mixed difficulty

The number of ways in which $n$ things of which $r$ are alike, can be arranged in a circular order, is

A student is allowed to select atmost $n$ books from a collection of $(2n + 1)$ books. If the number of ways in which he can do this, is 64, then the value of $n$ is

The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon, is

The number of four-letter words that can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is $R$, is

The sum of 4 digited numbers formed by using the digits $0,2,4,7,8$ without repetition is

A man invites 10 friends for a dinner party. In how many they can be seated around a circular table so that two particular friends on either side of man?

The number of ways of permuting the letters of the word DEVIL so that neither D is the first letter nor $\mathrm{L}$ is the last letter is

The number of combinations of 4 different objects $A, B, C$, $D$ taken 2 at a time is

The letters of the word 'HOSTEL' are arranged so that vowels occupy the end places. Then the number of arrangements is

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

The number of ways to 16 different things to three persons $A, B, C$ so that $B$ gets one more than $A$ and $C$ gets two more than $B$, is

The set $S=\{1,2,3, \ldots, 12\}$ to be partitioned into three sets $A, B, C$ of equal size. Thus,
$A \cup B \cup C=S, A \cap B=B \cap C=A \cap C=\phi$. The number of ways to partition $S$, is

The number of ways in which ten candidates $A_1, A_2, A_3, A_4, \cdots, A_{10}$ can be arranged in a row "If $A_1, A_2, A_3$ are sit together in a specified order is

The number of divisors a number 38808 can have, excluding 1 and the number itself is

The number of permutations of the letters of the word 'HINDUSTAN' such that neither the pattern 'HIN' nor 'DUS' nor 'TAN' appear, are

Eleven animals of a circus have to be placed in eleven cages one in each cage. If 4 of the cages are too small for 6 of the animals, then the number of ways of caging the animals is

If the number of ways of selecting $m$ cards out of unlimited number of cards bearing the number
2, 3, 4 so that they can not be used to write the number 423 is 93. Then $m$ is equal to

5- digit numbers are to be formed using $2,3,5,7,9$ without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $\mathrm{q}$ be the number of those that lie between 30000 and 90000 , then $p: q$ is :

The number of numbers greater than 50,000 that can be formed by using the digits $3,5,6,6,7,9$ is

6 white and 6 black balls are distributed among ten identical urns, so that there is atleast one ball in each urn. Balls are all alike except for the colour and each box can hold any number of balls. The number of different distributions of the balls is:

The number of ways that 8 beads of different colures be string as a necklace, is

The number of ways in which the six faces of a cube is painted with six different colours, is

There are 6 letters and 3 post-boxes. The number of ways in which these letters can be posted, is

There are 20 persons among whom two are brothers. The number of ways in which we can arrange them around a circle so that there is exactly one person between the brothers is

How many different words can be formed by Jumbling the letters in the word MISSISSIPPI in which no two S's are adjacent?

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

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

The letters of the word 'MEERUT' are arranged in all possible ways as in a dictionary, then the rank of the word 'MEERUT' is

Number of numbers between 5000 and 10000 by using the digits $1,3,5,7,9$ without repetition is equal to

8 different persons are sitting around a table. Numbers of ways in which we can select 3 of them so that no two are consecutive is