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  • Question
  • If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?


  • Options
  • A. 77
  • B. 66
  • C. 44
  • D. 55

  • Correct Answer
  • 66 

    Explanation

    first person will shake hands with 11 other persons. Seconds person will shake hands with 10 other persons, Third person will shake hands with 9 other person and so on.
    So , total handshake
    = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66

    OR

    2 person are to be chosen from 12 person to have a hand shake
    ? Possible ways = 12C2 = 12! / 2!(12 - 2)! = 66


  • Permutation and Combination problems


    Search Results


    • 1. 
      In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways can the three questions be selected?

    • Options
    • A. 1944
    • B. 2094
    • C. 1894
    • D. 2194
    • Discuss
    • 2. 
      139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round without actually playing in the first round. The pairing continues on the next round with a bye to any player left over. If the schedule is planned, so that a minimum number of matches is required to determine the champion, the number of matches which must be played is?

    • Options
    • A. 136
    • B. 137
    • C. 138
    • D. 139
    • Discuss
    • 3. 
      2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the five seats be occupied by these passengers?

    • Options
    • A. 15
    • B. 36
    • C. 48
    • D. 60
    • Discuss
    • 4. 
      Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat?

    • Options
    • A. 4!
    • B. 8!
    • C. 6!
    • D. 9!
    • Discuss
    • 5. 
      How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed?

    • Options
    • A. 3125
    • B. 625
    • C. 3905
    • D. 125
    • Discuss
    • 6. 
      Find the number of ways of preparing a chain with 5 different coloured beads?

    • Options
    • A. 18
    • B. 24
    • C. 12
    • D. 30
    • Discuss
    • 7. 
      Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women.?

    • Options
    • A. 30
    • B. 20
    • C. 10
    • D. 25
    • Discuss
    • 8. 
      Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each, so that there should be no identical series side by side and that the students sitting one behind the other should have the same series?

    • Options
    • A. 2 x 12C6 x (6!)2
    • B. 6! x 6!
    • C. 7! x 7!
    • D. None of these
    • Discuss
    • 9. 
      A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chosen?

    • Options
    • A. 112896
    • B. 3136
    • C. 720
    • D. 112
    • Discuss
    • 10. 
      A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?

    • Options
    • A. 320
    • B. 160
    • C. 80
    • D. 200
    • Discuss


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