Permutations an...

The maximum number of points of intersection of five lines and four circles is

From a group of persons the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is

If $$^nC_{r-1} = 36, \space ^nC_r = 84$$ and $$^nC_{r+1} = 126,$$ then find $$r$$.

If $$\displaystyle ^nC_{r-1}=56$$, $$\displaystyle ^nC_r=28$$ and $$\displaystyle ^nC_{r+1}=8$$ then r is equal to

The number of numbers of 9 different nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is 

In a packet there are m different books, n different pens and p different pencils. The number of selections of at least one article of each type from the packet is

The value of $$\displaystyle \sum_{r= 0}^{n}$$ $$\displaystyle ^{n+r}C_{r}$$ is equal to

For $$\displaystyle 2\leq r\leq n,\binom{n}{r}+2\binom{n}{r-1}+\binom{n}{r-2}$$ is equal to

The number of 5-digit even numbers that can be made with the digits 0,1,2 and 3 is

$$\displaystyle ^{n}C_{r+1}+^{n}C_{r-1}+2\times ^{n}C_{r}$$ is equal to