Permutations an...

A question paper on mathematics consists of twelve questions divided into three parts A, B and C, each containing four questions. In how many ways can an examinee answer five questions, selecting atleast one from each part.

There are $$k$$ different books and $$l$$ copies of each in a college library. The number of ways in which a student can make a selection of one or more books is

$$7$$ boys and $$8$$ girls have to sit in a row on $$15$$ chairs numbered from $$1$$ to $$15$$ then?

Number of different paths of shortest distance from A to B in the grid which do not pass through M.

A is a set containing n elements. A  subset P of A is chosen. The set A is reconstructed by replacing the element of P.A subset Q of A is again chosen. The number of way of choosing P and Q so that P Q =$$\phi $$ is :- 

A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is :

Given $$4$$ flags of different colours, how many different signals can be generated. If a signal requires the use of $$2$$ flags one below the other?

There are $$4$$ letter boxes in a post office. In how many ways can a man post $$8$$ distinct letters? 

$$4$$ buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are