Permutations an...

There are $$n$$ points on a circle. The number of staight lines formed by joining them is equal to

In a set of lottery Tickets $$7$$ carry prizes and $$25$$ are blank. If three tickets are drawn then the probability to get a prize is?

The sum of the numbers formed by taking all the digit at a from 0, 2, 3, 4 is 

Number of six digit numbers whose sum of the digits is $$49$$ are 

The letters of the word 'VICTORY' are arranged in all possible ways, and the words thus obtained are arranged as in a dictionary. Then the rank of given word is 

$$20$$ soldiers are standing in a row and their captain want to send $$7$$ out of them for a mission. In how many ways can captain select them such that at least one soldier find the soldier  next to him is also selected.   

If $$C_{r}$$ stands for $$^{n}C_{r}$$  then the sum of the series $$\frac{2(\frac{n}{2})!(\frac{n}{2})!}{n!}[C_{0}^{2}-2C_{1}^{2}+3C_{2}^{2}-.....+(-1)^{n}(n+1)C_{n}^{2}]$$,
where n is an even positive integer, is 

If $$^{32}C_{2n-1}=^{32}C_{n-3}$$ then $$n=$$

The value of $${ C }_{ 0 }^{ 2 }+3{ C }_{ 1 }^{ 2 }+5{ C }_{ 2 }^{ 2 }+.....$$ to $$n+1$$ terms is

The number of ways is which an examiner can assign $$30$$ marks to $$8$$ questions, giving not less Then $$2$$ marks to any question is-