Permutations and Combinations · Mathematics · MHT CET

A five digit number divisible by 3 is to be formed using the digits $0,1,2,3,4,5$ without repetition, then the total number of ways this can be done i...

Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked...

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least on...

The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is

_________ numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3.

Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be number of such words where no letter is repeated and $y$ b...

Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group if there ar...

Five persons $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and E are seated in a circular arangement, if each of them is given a hat of one of the ...

The number of ways in which 5 boys and 3 girls can be seated on a round table, if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacen...

A committee of 11 members is to be formed from 8 males and 5 females. If $m$ is the number of ways the committee is formed with at least 6 males and $...

The number of four letter words that can be formed using letters of the word BARRACK

Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the odd digits o...

If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are together and al...

If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are

A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the selection of a leader (from amon...

Five students are selected from $$n$$ students such that the ratio of number of ways in which 2 particular students are selected to the number of ways...

Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement. If each of them is given a ca...

The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are

If $$\mathrm{T}_{\mathrm{n}}$$ denotes the number of triangles which can be formed using the vertices of regular polygon of $$\mathrm{n}$$ sides and $...

The teacher wants to arrange 5 students on the platform such that the boy $$B_1$$ occupies second position and the girls $$G_1$$ and $$G_2$$ are alway...

Five students are to be arranged on a platform such that the boy $$B_1$$ occupies the second position and such that the girl $$G_1$$ is always adjacen...

A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if committee consists of at least 2 girls and a...

A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this group including the selection of...

If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged, then the number of mem...

If a question paper consists of 11 questions divided into two sections I and II. Section I consists of 6 questions and section II consists of 5 questi...

A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies are included, is

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are

The numbers can be formed using the digits $$1,2,3,4,3,2,1$$ so that odd digits always occupy odd places in __________ ways.

A polygon has 44 diagonals. Then the number of sides of the polygon are

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers....

The number of ways in which 8 different pearls can be arranged to form a necklace is

If $$\frac{n !}{2 !(n-2) !}$$ and $$\frac{n !}{4 !(n-4) !}$$ are in the ratio $$2: 1$$, then $$n=$$

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are togeth...