Maximum Value of nCr

Q. There are $n$ locks and $n$ matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trials required to open a lock.

1. None of the above
2. $\frac{n(n+1)}{2}$
3. $\frac{n(n+1)(n+2)}{6}$
4. $\frac{n(n-1)}{2}$

Q. A person wishes to make up as many different parties as he can out of 20 friends with the condition that each party consists of the same number. How many should he invite at a time?

1. 5
2. 10
3. 15
4. 20

Q. A person wishes to make up as many different parties as he can out of 20 friends with the condition that each party consists of the same number. How many should he invite at a time?

1. 5
2. 10
3. 15
4. 20

Q. A person wishes to make up as many different parties as he can out of 20 friends with the condition that each party consists of the same number. How many should he invite at a time?

1. 5
2. 10
3. 15
4. 20