Q: Two parallel lines each have a number of distinct points marked on them. On one line there are 2 points P and Q. On the other line there are 8 points. Find the number of different triangles which could be formed having 3 of the 10 points as vertices.
A: 64
Q: Out of 5 men and 3 women, a committee of 3 persons is to be formed. In how many ways can it be formed selecting at least 2 women?
A: 16
Q: From a group of 8 men and 4 women, 5 persons are to be selected to form a committee so that at least 2 women are there on the committee. In how many ways can it be done?
A: 457
Q: How many different words can be formed of the letters of the word “MATHEMATICS”, so that no two vowels are together?
A: (11!/2!*2!*2!) - (8!/2!*2!) * (4!/2!)
Q: In how many ways can the letters of the word KNOWLEDGE be rearranged so that the relative position of the vowels and consonants remain the same as in the word KNOWLEDGE?
A: 2160
Q: In how many combinations a cricketer can make a century with fours and sixes only?
A: 9
Q: The number of ways in which 6 different marbles can be put in two boxes of different sizes so that no box remains empty is
A: 62
Q: A cricket team coach while picking the playing XI for the finals, had different possibilities to choose players. The squad had 15 players in it, of which the coach had to choose only 11. Also due to consistent performance, the coach intends to include two specific players in the playing XI. With this condition, find how many ways in which the coach can select the playing XI ?
A: None of these
Q: The number of circles that can be drawn out of 10 points of which 7 are collinear is ________?
A: 85
Q: The number of five digit telephone number having at least one of their digits repeated is
A: 62784
Q: 3 books of mathematics and 5 books of physics are placed on a shelf so that the books on the same subject always remain together. The possible arrangements are
A: 1440
Q: In how many ways can a coach select 6 members out of 11 members, If a particular player should be always selected?
A: 10C5
Q: A family consists of a grandfather, 5 sons and daughters and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?
A: 8! x 480
Q: A forgetful teacher had the test papers and the marksheets of 5 students. But, he entered someone else’s marks for each of the 5 students. In how many different ways could he have made this error?
A: 44
Q: A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
A: 1260
Q: How many words can be made out of the letters of word ‘POUNDING’ such that all vowels occupy odd places?
A: 1440
Q: Four men and three women are to be seated in a row for a dinner such that no two women sit together and no two men sit together. Find the number of ways in which this can be arranged.
A: 144
Q: In how many ways can eight directors, Vice-chairman and chairman of a firm be seated in a round table, if the chairman has to sit between the Vice-chairman and a director?
A: 2 * 8!
Q: In an internal exam, there were 2 sections to be completed of which the 1st section contains 8 questions each with 4 choices and the second section contains 4 questions each with 5 choices. In how many different ways can the paper be answered if all the questions are attempted?
A: 48 × 54
Q: How many different ways are there to select 4 students for a team from 6 students of age 12 and 4 students of age 13, such that at least one student from age 12 group should be present in it?
A: 209
Q: At an election, there are five candidates out of which three members are to be elected, and a voter may vote for any number of candidates not greater than the number to be elected. Then the number of ways in which a voter may vote is
A: 25
Q: A box contains 2 white balls,3 black balls, and 4 red balls.In how many ways can 3 balls be drawn from the box,if at least one black ball is to be included in the draw?
A: 64
Q: A kid from 7th grade is very much interested in the chapter permutation and combination. While attending a class test, he came across a question that says " How many diagonals does a 7 sided polygon have". What will be the answer the kid must choose from the given option?
A: 14
Q: Find the number of ways in which 10 different diamonds can be arranged to make a necklace.
A: (1/2)*(9!)
Q: A box contains 7 red, 6 white and 4 blue balls. If 3 balls are randomly picked from the box and the red coloured ball should not be taken, then the number of ways of selecting is _____.
A: 120
Q: How many diagonals does a pentagon have and how many triangles can be formed with its vertices?
A: 5,10
Q: From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
A: 1260
Q: In a plane, there are 41 straight lines, of which 15 pass through point A and 9 pass through point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Find the number of points of intersection of the straight lines.
A: 681
Q: How many numbers can be formed from 1,2,3,4,5 (without repetition), so that the digit at the unit’s place must be greater than that the digit ten’s place?
A: 60
Q: A teacher while arranging 10 answer papers, has to arrange papers in such a way that the highest and the lowest score papers should never be together. In how many ways he can do this arrangement?
A: 8 × 9!