In rating 20 brands of cars, a car magazine picks a first,second,third,fourth and fifth best brand and then 7 more as acceptable, In how many ways can it be done?

A person wants to buy a car. There are two brands of car available in the market and each brand has 3 veriant models and each model comes in five different colours. In how many ways she can choose a car to buy?

A committee of 6 is to be choosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done?

An organization plans to plant saplings is 25 streets in a town in such a way that one sapling for the first street, three for the seconds, nine for the third and so on. How many sapling are needed to complete the work?

(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many was the person can select either an Indian or a Chinese food? (ii) There are 3 typesof toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train? (iii) How many of two-digit numbers can be formed using 1,2,3,4,5 without repetiton of digits? (iv) There persons enter in to a conference hall in which there are 10 seats, In how many ways they can take their place? (v) In how many ways 5 persons can be seated in a row?

A meeting hall has 30 rows in all. There are 20 seats in the first row, 24 seats in the second row and 28 seats in the third row and so on. How many seats are there in the hall?

(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?

There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in 15^(th) row and also find how many total seats are there in the auditorium?