Q: A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included one particular student?

Q: A party of ‘n’ persons sits at a round table. Find the odds against two specified persons sitting next to each other.

Q: A candidate takes up an entrance exam.There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions are from logical and has 4 choices each and the next two are from verbal and have 5 choices each each?

Q: How many different words can be formed of the letters of the word “MATHEMATICS”, so that no two consonants are together?

Q: Suppose Alice has 5 red balls and 4 green balls. She wants to arrange all the balls in a row in such a way that the red balls occupy the odd positions. How many arrangements are possible?

Q: The maximum number of points of intersection of 6 circles, is:

Q: In a party hall, 10 persons are to be arranged around a round table. If two particular persons are not to be seated side by side, then what is the total number of arrangements?

Q: Four pencils, three pens and five erasers are given to 5 boys and 7 girls such that1. no girl gets a pen.2. at least one of the boys should get an eraser and at least one boy should get a pencil.3. each person gets one item.In how many ways can the things be distributed if pencils, pens and erasers are of similar kind

Q: In how many ways the word PROBATION can be arranged so that two O's never come together?

Q: Two packs of 52 playing cards are shuffled together. Find the number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination.

Q: Mr. John has x children by his first wife and Ms. Bashu has x+1 children by her first husband. They marry and have children of their own. The whole family has 10 children. Assuming that two children of the same parents do not fight, find the maximum number of fights that can take place among children.

Q: The sum of all the numbers that can be formed with the digit 2,3,5,7 taken all at a time is

Q: Four men and three women are to be seated for a dinner in a row such that no two women sit together and no two men sit together. Find the number of ways in which this can be arranged.

Q: A tutor for primary education uses a trick to teach numbers to students. If she needs to teach numbers from 1 to 10, then she makes a piece of paper and writes down all the 10 numbers. She then picks a student at random and asks them to arrange any four-piece of papers in ascending order, so that students will know which number proceeds next. On the next day, the teacher missed number 2 and number 4 pieces of paper (which has got 2 and 4 written it respectively). Now in how many correct arrangements (ascending order) of four randomly chosen papers are possible?

Q:  In how many ways can 3 blue balls, 2 white balls and the rest 6 different colour balls be arranged in a row?

Q: In how many ways can 5 Americans and 5 Australian people be seated around a round table such that no two Americans are in adjacent positions?

Q: Out of 3 books on Economics, 4 books on Corporate strategy and 5 books on philosophy, what is the number of different collections of books if atleast one book on each subject is taken?

Q: Find the rank of the word “INDIA”

Q: How many five-letter words (with or without meaning) can be formed such that the letters appearing in the odd positions are taken from the non-repeated letters of the word CALCULATOR whereas the letters which occupy even places are taken from amongst the repeated letters of the same?

Q: Four different math, six different physics and two different chemistry textbooks are placed on a shelf. What is the number of possible combinations of arranging the textbooks if:The textbooks from each subject must be grouped together.

Q: A boy has five coins, each of a different value. How many different sums of money can be totaled with these five coins?

Q: Let Tn denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If Tn+1 – Tn = 21, then n equals

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two civil engineers will sit together?

Q: The actors of Bollywood plan a trip from Bombay to Goa. They decide to go by bus and arrange two buses Khatara and Sitara having 10 seats each. There are a total of 20 people. Five refuse to travel by Khatara as they don't like the name of the bus and six refuse to travel by Sitara. The number of ways in which these 20 can be seated in the two buses for the trip is

Q: There are 7 periods in each working day of a college. In how many ways can one organize 6 subjects such that each subject is allowed at least one period?

Q: Gowri needs to pick four cards, two each from two different decks of cards. Each deck will have 52 cards in it. The card that Gowri will pick should have all four different symbols present in a deck (Diamond, heart, spade, and club). What is the probability that Gowri will pick 4 different symbols?

Q: Vamsi has 6 Oreos and 7 Bourbon biscuits with him, which he decides to give to his friend. In how many ways Vamsi can give biscuits to his friend (given that at least one biscuit has to be given).

Q: In a chessboard, there are a number of tiles (squares) present in it which is painted only using two different colors (mostly black and white) at alternate places. How many squares are there in the chess board, if we do not consider the 1*1 tile?

Q: How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

Q: Pragg participates in a chess competition. All the pieces are fixed in their respective places while starting the game. In how many ways can he start the game?