$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

The students in a class are seated according to their marks in the previous examination. Once,it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement,the teacher wants to write down all possible arrangements,one in each of separate bits of paper,in order to choose one of these by lots. How many bits of paper are required?

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

In how many ways can a team of $11$ members be formed from a group of $15$ persons?