Permutations an...

A library has $$'a'$$ copies of one book, $$'b'$$ copies of each of two books, $$'c'$$ copies of each of three books, and single copy each of $$'d'$$. The total number of ways in which these books can be arranged in a row is

Total number of ways of selecting two numbers from the set $${1,2,3,...90}$$ so that their sum is divisible by $$3$$ is

In a certain examination paper, there are $$n$$ question. For $$j = 1, 2....n$$, there are $$2^{n-j}$$ students who answered $$j$$ or more questions wrongly. If the total number of wrong answers is $$4095$$, then the value of $$n$$ is:

The number of $$n$$ digit numbers which consists of the digits $$1$$ & $$2$$ only if each digits is to be used atleast once, is equal to $$510$$  then $$n$$ is equal to

Fill in the missing values.

Find the missing number, if same rule is followed in all the three figures.

The value of $$\displaystyle\sum^{10}_{r=0}(r)$$ $$^{20}C_r$$ is equal to?

Find the missing number in the given figure?

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is