Fundamental Principle 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

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

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?

A person can go from place '$A$' to '$B$' by $11$ different modes of transport but is allowed to return back to "$A$" by any mode other than the one earlier. The number of different ways, the entire journey can be complete is

A fruit basket contains $7$ apples, $6$ bananas and $4$ mangoes. How many selections of $3$ fruits can be made so that all $3$ are apples?

From a group of $8$ men and $4$ women, $4$ persons are to be selected to form a committee so that at least $2$ women are there on the committee. In how many ways can it be done?

Out of $7$ boys and $4$ girls a team of a debate club of $5$ is to be chosen. The number of teams such that each team includes at least one girl is ________ 

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have $4$ choices each and the next three have $2$ each?

Suppose a bakery has a selection of $20$ different cupcakes, $10$ different donuts, and $15$ different muffins. If you are to select a tasty treat, how many different choices of sweets can you choose from?

Suppose that we want to buy a computer from one of two makes $A_1$ and $A_2$. Suppose also that those makes have $12$ and $18$ different models, respectively. Then how many models are there altogether to choose from ?

A team consists of $6$ boys and $4$ girls and other has $5$ boys and $3$ girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?

If ${}^{10}\mathrm{c}_3+2.{}^{10}\mathrm{c}_4+{}^{10}\mathrm{c}_5={}^{\mathrm{n}}\mathrm{c}_5$ then the value of $\mathrm{n}=$