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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. 
      If the Price of 6 toys is Rs. 264.37, What will be the approximate price (Rs) of 5 toys?

    • Options
    • A. 230
    • B. 120
    • C. 320
    • D. 220
    • Discuss
    • 2. 
      A runs 1 2/ 3 times as fast as B. If A gives B a start of 40 m, how far must the winning post be, so that A and B might reach it at the same time?

    • Options
    • A. 75 m
    • B. 200 m
    • C. 100 m
    • D. 125 m
    • Discuss
    • 3. 
      A person rows a kilometre down the stream in 10 minute and upstream in 30 minutes. Find the velocity of the stream?

    • Options
    • A. 1 km/hr
    • B. 2 km/hr
    • C. 3 km/hr
    • D. 4 km/hr
    • Discuss
    • 4. 
      One year ago the ratio between Samir and Ashok's age was 4 : 3. One years Later the sum of their ages will be 5 : 4. What is the sum of their present ages in years?

    • Options
    • A. 12 years
    • B. 15 years
    • C. 16 years
    • D. Cannot be determined
    • Discuss
    • 5. 
      What is 786 time of 964?

    • Options
    • A. 759276
    • B. 749844
    • C. 75416
    • D. 757704
    • Discuss
    • 6. 
      The percent profit when an article is sold for Rs. 78 is twice as when it is sold for Rs. 69. The C.P. of the article is?

    • Options
    • A. Rs. 49
    • B. Rs. 51
    • C. Rs. 57
    • D. Rs. 60
    • Discuss
    • 7. 
      In a game of 100 points, A scores 100 points while B scores only 65 points. In this game, how much points can A give to B?

    • Options
    • A. 45
    • B. 35
    • C. 25
    • D. 55
    • Discuss
    • 8. 
      Find the value of log 8 + log 1/8?

    • Options
    • A. 0
    • B. 1
    • C. 2
    • D. log (64)
    • Discuss
    • 9. 
      Given log 10 2 = 0.30103, log 10 3 = 0.47712. Find the number of digit, in 3 12 x 2 8?

    • Options
    • A. 6
    • B. 7
    • C. 8
    • D. 9
    • Discuss
    • 10. 
      Find the product of place value and face value of 5 in 65231

    • Options
    • A. 28000
    • B. 25000
    • C. 27000
    • D. 26000
    • Discuss


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