Permutation and combination practice · Easy

The lock of a safe consists of five discs each of which features the digits 0, 1, 2, … ,9.The safe can be opened by dialing a special combination of the digits. The number of days sufficient enough to open the safe. If the work day lasts 13 h and 5 s are needed to dial one combination of digits is

The product of $r$ consecutive positive integers is divisible by

In a steamer there are stalls for 12 animals and there are cows, horses and calves (not less than 12 of each) ready to be shipped. The total number of ways in which the ship load can be made 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

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

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

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

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

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

If $f:\{1,2,3,4,5\} \rightarrow\{x, y, z, t\}$, then the total number of onto functions is equal to

Find the number of ways of arranging 6 boys and 6 girls around a circle

The number of different 7 digit numbers that can be written using only the three digits 1,2 and 3 with the condition that the digit 2 occurs twice in each number is

Let $A$ be the set of four digit numbers $a_1 a_2 a_3 a_4$, where ${a_1} > {a_2} > {a_3} > {a_4}$, then $n(A)$ is

The letters of the word "CONTINUE" are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangements is

Out of 10 consonants four vowels, the number of words that can be formed using six consonants and three vowels

The number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is