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Home Aptitude Permutation and Combination Comments

  • Question
  • The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a group consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is


  • Options
  • A. 1960
  • B. 3240
  • C. 1540
  • D. None of these

  • Correct Answer
  • None of these 

    Explanation

    If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or if Mrs. X is not selected then Mr. Y can be there in the committee...
    So, required number of ways
    = 8C3 x 6C4 + 7C3 x 7C4
    = [(8 x 7 x 6)/(3 x 2)] x [(6 x 5)/(2 x 1)] + [(7 x 6 x 5)/(3 x 2)] x [(7 x 6 x 5)/(3 x 2)]
    = 840 + 1225
    = 2065


  • Permutation and Combination problems


    Search Results


    • 1. 
      There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities, is

    • Options
    • A. 92
    • B. 90
    • C. 91
    • D. 93
    • Discuss
    • 2. 
      A question paper consists of two sections having respectively 3 and 5 questions. The following note is given on the paper. "It is not necessary to attempt all the question". One question from each section is compulsory. In how many ways, a candidate can select the question?

    • Options
    • A. 38
    • B. 217
    • C. 256
    • D. 320
    • Discuss
    • 3. 
      There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points .

    • Options
    • A. 364
    • B. 360
    • C. 368
    • D. 365
    • Discuss
    • 4. 
      In how many ways, can 24 persons be seated around a circular table if there are is 13 seats?

    • Options
    • A. 24! / [13 x 11! ]
    • B. 22! / [14 x 12!]
    • C. 23! / [13 x 11!]
    • D. 24! / [12 x 12!]
    • Discuss
    • 5. 
      There is a 7-digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone number are possible?

    • Options
    • A. 120
    • B. 100000
    • C. 6720
    • D. 30240
    • Discuss
    • 6. 
      A five-digit number divisible by 3 is to be formed using digits 0, 1, 2, 3, 4 and 5 without repetition, the total number of ways this can be done, is

    • Options
    • A. 122
    • B. 210
    • C. 216
    • D. 217
    • Discuss
    • 7. 
      A new flag is to be designed with six vertical stripes using some or all of the colour yellow, green,blue and red. Then, the number of ways this can be made such that no two adjacent stripes have the same colour is

    • Options
    • A. 12 x 81
    • B. 16 x 192
    • C. 20 x 125
    • D. 24 x 216
    • Discuss
    • 8. 
      An intelligence agency forms a code of two distinct digits selected from 0, 1, 2,....., 9 such that the first-digit of code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down, for examples the code 91 may appear as 16. how many codes are there for which no such confusion can arise?

    • Options
    • A. 80
    • B. 78
    • C. 71
    • D. 69
    • Discuss
    • 9. 
      How many numbers can be formed from 1, 2, 3, 4, 5, ( without repetition), when the digit at the unit's place must be greater than that in the ten's place?

    • Options
    • A. 54
    • B. 60
    • C. 51/3
    • D. 2 x 4!
    • Discuss
    • 10. 
      Boxes numbered 1, 2, 3, 4, and 5 are kept in a row and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

    • Options
    • A. 8
    • B. 10
    • C. 15
    • D. 22
    • Discuss


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