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  • Question
  • In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?


  • Options
  • A. 36
  • B. 25
  • C. 24
  • D. 72

  • Correct Answer
  • 25 

    Explanation

    The toys are different; The boxes are identical 

     

    If none of the boxes is to remain empty, then we can pack the toys in one of the following ways 

    a. 2, 2, 1 

    b. 3, 1, 1 

     

    Case a. Number of ways of achieving the first option 2 - 2 - 1 

     

    Two toys out of the 5 can be selected in  5 C 2  ways. Another 2 out of the remaining 3 can be selected in  3 C 2  ways and the last toy can be selected in  1 C 1  way. 

     

    However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2 

     

    Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways 5 C 2 * 3 C 2 = 15 ways

     

     

    Case b. Number of ways of achieving the second option 3 - 1 - 1

     

    Three toys out of the 5 can be selected in  5 C 3  ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.

     

    Therefore, total number of ways of getting the 3 - 1 - 1 option is  5 C 3  = 10 = 10 ways.

     

     

     

    Total ways in which the 5 toys can be packed in 3 identical boxes

     

    = number of ways of achieving Case a + number of ways of achieving Case b= 15 + 10 = 25 ways.


  • More questions

    • 1. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 2. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 3. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss
    • 4. 
      Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?

    • Options
    • A. {3, 4} ? A
    • B. {3, 4} ? A
    • C. 1 ? A
    • D. {1, 2, 5} ? A
    • Discuss
    • 5. 
      Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 4 : 5
    • D. 7 : 3
    • Discuss
    • 6. 
      1, 2, 4, 8, 16, 32, 64, (...), 256?

    • Options
    • A. 148
    • B. 128
    • C. 154
    • D. 164
    • Discuss
    • 7. 
      A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

    • Options
    • A. 150 m
    • B. 200 m
    • C. 125 m
    • D. 115 m
    • Discuss
    • 8. 
      8% of 96 =? of 1/25

    • Options
    • A. 19.2
    • B. 7.68
    • C. 1.92
    • D. None of these
    • Discuss
    • 9. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

    • Options
    • A. Rs. 35
    • B. Rs. 245
    • C. Rs. 350
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 10. 
      If the hands of a clock coincide in every 65 minutes (true time), in 24 hours the clock will gain:

    • Options
    • A. 10 10 minutes. 143
    • B. 9 12 minutes. 143
    • C. 11 12 minutes. 143
    • D. 12 10 minutes. 143
    • Discuss


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