logo

CuriousTab

CuriousTab

Discussion


Home Aptitude Permutation and Combination See What Others Are Saying!
  • 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. The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

    • Options
    • A. 5 : 7
    • B. 4 : 9
    • C. 1 : 1
    • D. 4 : 7
    • Discuss
    • 2. In a mixture of 35 litres, the ratio of milk and water is 4:1. If 7 litres of water is added to the mixture, the ratio of milk and water of the new mixture will be

    • Options
    • A. 2:1
    • B. 1:2
    • C. 4:5
    • D. 5:4
    • Discuss
    • 3. 
      If the three- fourth of number is subtracted from the number, the value so obtained is 163. What is that number?

    • Options
    • A. 625
    • B. 562
    • C. 632
    • D. 652
    • Discuss
    • 4. 8 litres are drawn from a flask containing milk and then filledwith water. The operation is performed 3 more times. Theratio of the quantity of milk left and total solution is 81/625.How much milk the flask initially holds?

    • Options
    • A. 10 ltr
    • B. 20 ltr
    • C. 30 ltr
    • D. 40 ltr
    • Discuss
    • 5. The square root of 64009 is:

    • Options
    • A. 253
    • B. 347
    • C. 363
    • D. 803
    • Discuss
    • 6. 4, -8, 16, -32, 64, (....)

    • Options
    • A. 128
    • B. -128
    • C. 192
    • D. -192
    • Discuss
    • 7. 
      6.39 x 128.948 + 5.215 ÷ 12.189 + 25.056 =?

    • Options
    • A. 800
    • B. 900
    • C. 850
    • D. 950
    • Discuss
    • 8. 
      A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?

    • Options
    • A. 48
    • B. 60
    • C. 56
    • D. 64
    • Discuss
    • 9. 
      If 1 / 3.718 = .2689, then the value of 1 / .0003718 is?

    • Options
    • A. 2689
    • B. 2.689
    • C. 26890
    • D. .2689
    • Discuss
    • 10. 
      A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the same piece of work is?

    • Options
    • A. 10
    • B. 15
    • C. 12
    • D. 9.6
    • Discuss


    Comments

    There are no comments.

Enter a new Comment