Evaluate

There are 18 points in a plane of which 5 are collinear. How many straight lines can be formed by joining them?

Find the number of ways in which a committee of 2 teachers and 3 students can be formed out of 10 teachers and 20 students. In how many of these committees
(i)a particular teacher is included?
(ii)a particular student is included?
(iii)a particular student is excluded?

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 without repetition?

How many different selections of 4 books can be made from 10 different books, if
(i)there is no restriction?
(ii)two particular books are always selected?
(iii)two particular books are never selected?

How many triangles can be formed in a decagon?

How many triangles can be obtained by joining 12 points, four of which are collinear?

Find the number of diagonals of
(i)a hexagon,
(ii)a decagon,
(iii)a polygon of 18 sides

Find the number of 5-card combinations out of a deck of 52 cards if a least one of the five cards has to be king.

From a class of 14 boys and 10 girls, 10 students are to be chosen for a competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways can this be done, when (i) at least 2 ladies are included? (ii) at most 2 ladies are included?

A committee of three persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?