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  • Question
  • From a group of 7 boys and 6 girls, five persons are to be selected to form a team, so that at least 3 girls are there in the team. In how many ways can it be done?


  • Options
  • A. 427
  • B. 531
  • C. 651
  • D. 714

  • Correct Answer
  • 531 

    Explanation

    Given in the question that, there are 7 boys and 6 girls. 

    Team members = 5

    Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

    6 C 3     x   7 C 2     +   6 C 4   x   7 C 1   +   6 C 5 =   6 x 5 x 4 3 x 2 x 1   x   7 x 6 2 x 1   +   6 x 5 x 4 x 3 4 x 3 x 2 x 1   x   7   +   6 x 5 x 4 x 3 x 2 5 x 4 x 3 x 2 x 1 =   420   +   105   +   6 =   531 .

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    Permutation and Combination problems


    Search Results


    • 1. The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?

    • Options
    • A. 2(6!)
    • B. 6! x 7
    • C. 6! x ?P?
    • D. None
    • Discuss
    • 2. How many three digit numbers 'abc' are formed where two of the three digits are same ?

    • Options
    • A. 252
    • B. 648
    • C. 243
    • D. 900
    • Discuss
    • 3. Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?

    • Options
    • A. 28
    • B. 56
    • C. 44
    • D. 36
    • Discuss
    • 4. There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?

    • Options
    • A. 1000
    • B. 625
    • C. 525
    • D. 125
    • Discuss
    • 5. A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?

    • Options
    • A. 142
    • B. 175
    • C. 212
    • D. 253
    • Discuss
    • 6. In a plane 8 points are colliner out of 12 points, then the number of triangles we get with those 12 points is

    • Options
    • A. 20
    • B. 160
    • C. 164
    • D. 220
    • Discuss
    • 7. There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays ?

    • Options
    • A. 12400
    • B. 17820
    • C. 17280
    • D. 12460
    • Discuss
    • 8. How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

    • Options
    • A. 1000
    • B. 100
    • C. 500
    • D. 999
    • Discuss
    • 9. A polygon 7 sides.How many diagonals can be formed?

    • Options
    • A. 14
    • B. 7
    • C. 15
    • D. 21
    • Discuss
    • 10. If there are 15 dots on a circle,how many triangles can be formed?

    • Options
    • A. 455
    • B. 450
    • C. 469
    • D. 500
    • Discuss


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