Fundamental Principles of Counting

If $15$ people won prizes in the state lottery (assuming that there are no ties), how many ways can these $15$ people win first, second, third, fourth and fifth prizes?

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

G. Nath StoresL. R. ChowkKota -324002

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

Yogi chaphriderNiranjan AshramNaseek -422013

How many permutations can be made out of the letters in the word island taking four letters at a time?

Inequalities in which items compared are never equal to each other is classified as

Five friends Lalit, Feroz, Shahid, John and Manjeet are painter, Singer, Dancer, Poet or Sculptor. Lalit and Feroz are not Sculptor or Dancer. John and Manjeet are not Poet or Painter. Shahid is neither Painter nor Dancer. Manjeet is not a Dancer. Feroz and Shahid are not Poet or Singer. Who is Poet?

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

E.T.N. HospitalZahermargBilandoli Garden

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

Phiroz GerablHarmit palaceSamaita nagar

Five different Mathematics books,$4$ different electronics books, and $2$different communications books are to be placed on a shelf with the books of the same subject together. Find the number of ways in which the books can be placed?

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

B. K. BhushanAnant jeweller'sK hajureth-4711606

A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?

In each question below a combination of name and address is given, followed by four such options, one each under the columns A,B, C and D. You have to find out the combination which is exactly the same as the combination in the question. The number of that option which contains that combination is the answer.

Nitu gajadharShersing HaveliJaipur -302006

In how many ways can $4$ boys and $4$ girls be seated alternately in a row of $8$ seats?

There are $15$ students in a group and among them $9$ are boys and the remaining are girls. From this group $5$ students to be selected for a competition and at least $3$ should be girls. In how many ways can it be done?

Let $E\left(n\right)$ denotes the sum of the even digits of $n$. For example $E\left(1243\right)=2+4=6$, then the value of $E\left(1\right)+E\left(2\right)+E\left(3\right)+\mathrm{.....}+E\left(100\right)$ is equal to

Consider $5$ straight lines in a plane such that no two of them are parallel and no three of the them intersect at a point. Then, the number of disjoint regions into which the plane is divided by these lines equals to

Which of the following statements is correct regarding the statement given below?

The five-digit numbers can be formed from the first four prime numbers.

For a given matrix, let $R_i$, denote the sum of all entries in its $i^{th}$ row and $C_j$ denote the sum of all entries in its $j^{th}$ column. How many $3\times 3$ matrices with non-negative integer entries are there such that $R_1=R_2=C_1=C_2=2$ and $R_3=C_3=1?$