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  • Question
  • If 7 points out of 12 are in the same straight line, then the number of triangles formed is?


  • Options
  • A. 19
  • B. 158
  • C. 185
  • D. 201

  • Correct Answer
  • 185 

    Explanation

    The number of ways of selecting 3 points out of 12 points is 12C3. The number of ways of selecting 3 points out of 7 points, on the same straight line is 7C3, Hence, the number of triangle formed will be 12C3 - 7C3 = 210 - 35 = 185.


  • Permutation and Combination problems


    Search Results


    • 1. 
      If S= {2, 3, 4, 5, 7, 9} , then the number of different three-digit number (with all distinct digits) less than 400 that can be formed from S is?

    • Options
    • A. 20
    • B. 40
    • C. 80
    • D. 120
    • Discuss
    • 2. 
      If nP r= 720 nC r than the value r is?

    • Options
    • A. 6
    • B. 5
    • C. 4
    • D. 7
    • Discuss
    • 3. 
      If 2n + 1P n - 1 : 2n - 1P n = 3 : 5, then n is equal to?

    • Options
    • A. 4
    • B. 6
    • C. 3
    • D. 8
    • Discuss
    • 4. 
      If 35C n + 7 = 35C 4n - 2, then all the values of n are given by?

    • Options
    • A. 28
    • B. 3, 6
    • C. 3
    • D. 6
    • Discuss
    • 5. 
      If nC r - 1 = 36, nC r = 84 and nC r + 1 = 126 then?

    • Options
    • A. n = 8, r = 4
    • B. n = 9, r = 3
    • C. n = 7, r = 5
    • D. None of these
    • Discuss
    • 6. 
      In how many different ways can the letters of word JUDGE be arranged so that the vowels always come together?

    • Options
    • A. 48
    • B. 24
    • C. 120
    • D. 60
    • Discuss
    • 7. 
      From 4 officers and 8 Jawans in how many ways can 6 be chosen to include at least one officer?

    • Options
    • A. 896
    • B. 986
    • C. 886
    • D. 996
    • Discuss
    • 8. 
      From a group of 6 men and 4 women a committee of 4 persons is to be formed?

    • Options
    • A. 210
    • B. 225
    • C. 195
    • D. 185
    • Discuss
    • 9. 
      The numbers of straight lines can be formed out of 10 points of which 7 are collinear?

    • Options
    • A. 26
    • B. 21
    • C. 25
    • D. None of these
    • Discuss
    • 10. 
      The number of different permutations of the word 'BANANA' is?

    • Options
    • A. 270
    • B. 60
    • C. 120
    • D. 360
    • Discuss


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