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  • Question
  • 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 many 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

  • Correct Answer
  • 22 

    Explanation

    Total number of ways of filling the 5 boxes numbered as (1, 2, 3, 4, and 5) with either blue or red balls 25 = 32.
    Two adjacent boxes with blue can be obtained in 4 ways, i.e., (12), (23), (34) and (45).
    Three adjacent boxes with blue can be obtained in 3 ways, i.e., (123), (234)and (345). Four boxes with blue can be obtained in 2 ways, i.e., (1234) and (2345). And five boxes with blue can be got in 1 way. Hence, the number of ways of filling the boxes such that adjacent boxes have blue
    = (4 + 3 + 2 + 1) = 10.
    Hence, the number or ways of filling up the boxes such that no two adjacent boxes have blue = 32 - 10 = 22.


  • More questions

    • 1. 
      An elevator starts with 5 passengers and stops at 8 different floors if the house. Find out the probability of all the 5 passengers alighting at different floors.

    • Options
    • A. 101/512
    • B. 105/512
    • C. 107/512
    • D. 109/512
    • Discuss
    • 2. 
      A single discount equivalent to three successive discounts of 5% , 10% , 20% is :

    • Options
    • A. 68.4 %
    • B. 35 %
    • C. 31.6 %
    • D. 32 %
    • Discuss
    • 3. 
      The discount on $ 5229 due in 1 year 9 months reckoning compound interest at 5 % is :

    • Options
    • A. $ 429.00
    • B. $ 415.00
    • C. $ 393.25
    • D. None of these
    • Discuss
    • 4. 
      If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :

    • Options
    • A. $ 20
    • B. $ 21.81
    • C. $ 22
    • D. $ 18.33
    • Discuss
    • 5. 
      ?. 10x 2 ? 7x + 1 = 0
      ?. 35y 2 -12y + 1 = 0

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 6. 
      Abhinav save Rs. 25 by getting 6.66% discount on a textbook.What is the amount of money (in Rs.) paid by him?

    • Options
    • A. 450
    • B. 350
    • C. 225
    • D. 375
    • Discuss
    • 7. 
      ?. x 3 - 371 = 629
      ?. y 3 - 543 = 788

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 8. 
      The roots of the equation a2x2 - 3abx + 2b2 = 0 are

    • Options
    • A. 2b , - b a a
    • B. 2b , b a a
    • C. - 2b , - b a a
    • D. None of these
    • Discuss
    • 9. 
      1, 8, 27, 64, 125, 216, (...) :

    • Options
    • A. 354
    • B. 343
    • C. 392
    • D. 245
    • Discuss
    • 10. 
      The Different between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is

    • Options
    • A. 2520 m2
    • B. 2480 m2
    • C. 2420 m2
    • D. None of these
    • Discuss


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