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Permutations and Combinations

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  1. 101.The number of elements in the set S = (r,k) : k Z and 36r+1 = 635rk^2-3 is:
  2. 102.A building has ground floor and 10 more floors.
  3. 103.If the number of seven-digit numbers such that the sum of their digits is even is m n 10^n…
  4. 104.All five-letter words are made using all the letters A, B, C, D, E and arranged as in an E…
  5. 105.Let m and n, (m<n), be two 2-digit numbers.
  6. 106.In a group of 3 girls and 4 boys, there are two boys B_1 and B_2.
  7. 107.Let A(4 t, 4 t), B(2 t, -2 t) and C(3r-n, r^2-n-1) be the vertices of a triangle ABC, wher…
  8. 108.Let P be the set of seven-digit numbers with sum of digits equal to 11, formed using only …
  9. 109.The number of ways in which the letters A, B, C, D, E can be placed in the 8 boxes of the …
  10. 110.Line L_1 of slope 2 and line L_2 of slope 12 intersect at the origin O.
  11. 111.From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which sho…
  12. 112.There are 12 points in a plane, no three of which are collinear, except 5 points which are…
  13. 113.In an examination of Mathematics paper, there are 20 questions of equal marks and the ques…
  14. 114.The lines L_1, L_2, , L_20 are distinct.
  15. 115.The number of 9 digit numbers that can be formed using all the digits of the number 123412…
  16. 116.A boy needs to select five courses from 12 available courses, out of which 5 courses are l…
  17. 117.The number of integers greater than 7000 that can be formed using the digits 3, 5, 6, 7, 8…
  18. 118.Let S=1,2,3,5,7,10,11.
  19. 119.If all the six digit numbers x_1x_2x_3x_4x_5x_6 with 0<x_1<x_2<x_3<x_4<x_5<x_6 are arrange…
  20. 120.Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, …
  21. 121.Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetition, and are writ…
  22. 122.The number of 3 digit numbers that are divisible by either 3 or 4 but not divisible by 48,…
  23. 123.The letters of the word OUGHT are written in all possible ways and these words are arrange…
  24. 124.The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is ______.
  25. 125.Number of 4-digit numbers (repetition allowed) which are made using the digits 1, 2, 3 and…
  26. 126.Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or…
  27. 127.Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allow…
  28. 128.Number of integral solutions to the equation x+y+z=21, where x1, y3, z4, is equal to _____…
  29. 129.The total number of six digit numbers formed using the digits 4, 5, 9 only and divisible b…
  30. 130.The number of ways of giving 20 distinct oranges to 3 children such that each child gets a…
  31. 131.A person forgets his 4-digit ATM pin code.
  32. 132.The letters of the word 'MANKIND' are written in all possible orders and arranged in seria…
  33. 133.The number of 5-digit natural numbers, such that the product of their digits is 36, is ___…
  34. 134.Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits…
  35. 135.Let S be the sample space of all five digit numbers.
  36. 136.Let S be the set of all passwords which are six to eight characters long, where each chara…
  37. 137.A class contains b boys and g girls.
  38. 138.Let S=4,6,9 and T=9,10,11,,1000.
  39. 139.The number of natural numbers lying between 1012 and 23421 that can be formed using the di…
  40. 140.In an examination, there are 5 multiple choice questions with 3 choices, out of which exac…
  41. 141.The number of 7-digit numbers which are multiples of 11 and are formed using all the digit…
  42. 142.The sum of all the elements of the set 1,2,,100 : (,24)=1 is ___ Answer: 1633
  43. 143.The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is____ Answer: …
  44. 144.The total number of three-digit numbers, with one digit repeated exactly two times, is___ …
  45. 145.There are ten boys B_1,,B_10 and five girls G_1,,G_5 in a class.
  46. 146.The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is____ An…
  47. 147.The number of ways 16 identical cubes, of which 11 are blue and rest are red, can be place…
  48. 148.The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without r…
  49. 149.Let A=1,a_1,a_2,,a_18,77 be a set of integers with 1<a_1<a_2<<a_18<77.
  50. 150.The number of ways to distribute 30 identical candies among four children C_1,C_2,C_3,C_4 …