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. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

    • Options
    • A. 2 : 3
    • B. 1 : 1
    • C. 3 : 4
    • D. 4 : 3
    • Discuss
    • 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

    • Options
    • A. 65 sec
    • B. 89 sec
    • C. 100 sec
    • D. 150 sec
    • Discuss
    • 3. What was the day of the week on 17th June, 1998?

    • Options
    • A. Monday
    • B. Tuesday
    • C. Wednesday
    • D. Thursday
    • Discuss
    • 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

    • Options
    • A. 279
    • B. 283
    • C. 308
    • D. 318
    • Discuss
    • 5. 
      1872/ ? ? = 234

    • Options
    • A. 324
    • B. 64
    • C. 8
    • D. 256
    • Discuss
    • 6. 
      For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?

    • Options
    • A. 15 : 14
    • B. 16 :15
    • C. 12 :11
    • D. 10 : 9
    • Discuss
    • 7. 
      A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?

    • Options
    • A. 34%
    • B. 46%
    • C. 54%
    • D. 66%
    • Discuss
    • 8. 
      1, 9, 25, 49, 81,?

    • Options
    • A. 90
    • B. 135
    • C. 121
    • D. 125
    • Discuss
    • 9. 
      An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?

    • Options
    • A. 7:30
    • B. 6:30
    • C. 8:00
    • D. 9:30
    • Discuss
    • 10. 
      P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?

    • Options
    • A. Tuesday
    • B. Friday
    • C. Wednesday
    • D. Sunday
    • Discuss


    Comments

    There are no comments.

Enter a new Comment