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  • Question
  • A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?


  • Options
  • A. 32
  • B. 48
  • C. 64
  • D. 96
  • E. None of these

  • Correct Answer
  • 64 

    Explanation
    We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

    ∴ Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
    = 3 x 6 x 5 + 3 x 2 x 6 + 1
    2 x 1 2 x 1
    = (45 + 18 + 1)
    = 64.


    Permutation and Combination problems


    Search Results


    • 1. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

    • Options
    • A. 120
    • B. 720
    • C. 4320
    • D. 2160
    • E. None of these
    • Discuss
    • 2. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

    • Options
    • A. 40%
    • B. 42%
    • C. 44%
    • D. 46%
    • Discuss
    • 3. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

    • Options
    • A. Rs. 456
    • B. Rs. 458
    • C. Rs. 558
    • D. Rs. 568
    • Discuss
    • 4. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

    • Options
    • A. 1520 m2
    • B. 2420 m2
    • C. 2480 m2
    • D. 2520 m2
    • Discuss
    • 5. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

    • Options
    • A. 16 cm
    • B. 18 cm
    • C. 24 cm
    • D. Data inadequate
    • E. None of these
    • Discuss
    • 6. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

    • Options
    • A. 210
    • B. 1050
    • C. 25200
    • D. 21400
    • E. None of these
    • Discuss
    • 7. In how many ways can the letters of the word 'LEADER' be arranged?

    • Options
    • A. 72
    • B. 144
    • C. 360
    • D. 720
    • E. None of these
    • Discuss
    • 8. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

    • Options
    • A. 32
    • B. 48
    • C. 36
    • D. 60
    • E. 120
    • Discuss
    • 9. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

    • Options
    • A. 360
    • B. 480
    • C. 720
    • D. 5040
    • E. None of these
    • Discuss
    • 10. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

    • Options
    • A. 266
    • B. 5040
    • C. 11760
    • D. 86400
    • E. None of these
    • Discuss


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