Combination

In how many ways can a committee of 4 be selected from a group of 9 persons?

There are 6 distinct points on a circle. How many inscribed triangles can be drawn using the six points as vertices?

How many teams of at least 3 students and at most 6 students can be chosen from 10 students?

How many diagonals does a decagon have?

In how many ways can a patrol of 1 officer and 4 enlisted men be chosen from 4 officers and 10 enlisted men?

In how many ways can a delegation of 7 students be chosen from 5 seniors, 5 juniors, 4 sophomores, and 3 freshmen if the delegation includes 2 seniors, 2 juniors, 2 sophomores and 1 freshman?

Find the value of n if C(n, 2) =C(n,8).

In how many ways can a set of 3 mathematics books and 2 physics books be chosen from 6 different mathematics books and 5 different physics books?

Find n if C(n+2,4)=C(n, 2).

At a party, each guest shook hands with every other guest exactly once. There were a total of 1225 handshakes. How many guests were there?