A person tries to form as many different parties as he can, out of his 20 friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

(i) A kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court? (ii) There are 15 persons in a party and if , each 2 of them shakes hands wit each with each other. How many handshakes happen in the party? (iii) How many chords can be drawn through 20 points on a circle? (iv) In a parking lot one hunderd, one year old cars are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars are possible? (v) How many ways can a team of 3 boys, 2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgender?

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

There are 15 persons in a party and if each 2 of then shakes hands with each other , how many handshakes happen in the party ?

A number of four different digits is formed with the use of the digits 1,2,3,4 and 5 in all possible ways. Find the following (i) How many such numbers can be formed? (ii) How many of these are even? (iii) How many of these are exactly divisible by 4?

In how many different ways may 12 things, 4 each of three varieties be distributed equally among two persons? Things of the same variety are assumed to be identical.