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  • Question
  • 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

  • Correct Answer
  • 160 

    Explanation

    3 girls can be be selected out of 5 girls in 5C3 ways. Since, number of boys to be invited is not given, hence out of 4 boys, he can invite them in (2)4 ways.
    ? Required number of ways 5C3 x (2)4 = 10 x 16 = 160


  • Permutation and Combination problems


    Search Results


    • 1. 
      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
    • 2. 
      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
    • 3. 
      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
    • 4. 
      Find the number of ways of preparing a chain with 5 different coloured beads?

    • Options
    • A. 18
    • B. 24
    • C. 12
    • D. 30
    • Discuss
    • 5. 
      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
    • Discuss
    • 6. 
      In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

    • Options
    • A. 9
    • B. 12
    • C. 14
    • D. 18
    • Discuss
    • 7. 
      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 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
    • 8. 
      A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets?

    • Options
    • A. 12
    • B. 64
    • C. 256
    • D. 60
    • Discuss
    • 9. 
      In how many ways, can the letters of the word 'ASSASSINATION' be arranged, so that all the S are together?

    • Options
    • A. 10!
    • B. 14! (4!)
    • C. 151200
    • D. 3628800
    • Discuss
    • 10. 
      Find the number of ways, in which 12 different beads can be arranged to form a necklace .

    • Options
    • A. 11 !/2
    • B. 10 !/2
    • C. 12 !/2
    • D. Couldn't be determined
    • Discuss


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