There are $10$ bulbs in a room. Each of them can be switched on independently. In how many ways can the room be illuminated?

The difference between the maximum value of ${}^6C_r$ and ${}^nC_3$ is $16$. Then $n=$

In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?

The number of ways in which $16$ identical oranges can be distributed among $4$ children such that each child gets at least one orange is:

The number of ways $16$ identical cubes,of which $11$ are blue and the rest are red,can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes,is

Out of $6$ books,in how many ways can a set of one or more books be chosen?