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  • Question
  • In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?


  • Options
  • A. 159
  • B. 194
  • C. 205
  • D. 209
  • E. None of these

  • Correct Answer
  • 209 

    Explanation
    We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

    ∴ Required number
    of ways
    = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
    = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
    = (6 x 4) + 6 x 5 x 4 x 3 + 6 x 5 x 4 x 4 + 6 x 5
    2 x 1 2 x 1 3 x 2 x 1 2 x 1
    = (24 + 90 + 80 + 15)
    = 209.


    More questions

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      The product of two consecutive odd numbers is 19043. Which is the smaller one?

    • Options
    • A. 137
    • B. 131
    • C. 133
    • D. 129
    • Discuss
    • 2. 
      The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :

    • Options
    • A. b tan ? cosec B
    • B. a tan ? cosec A 2
    • C. c tan ? cosec C 2
    • D. None of these
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    • 3. 
      From a point on a circular tract 5 Km long A, B and C started running in the same direction at the same time with speeds of 2 1? 2 Km/h, 3 Km/h and 2 Km/h. respectively. Then on the starting point all three will meet again after :

    • Options
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    • 4. 
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    • Options
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    • B. 31.68 km/hr.
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    • 5. 
      A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated?

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    • Options
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