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. 15
  • B. 10
  • C. 25
  • D. 20

  • 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 5 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:

    5 C 2 * 3 C 2 2 = 10 * 3 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 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. 
      0.0169 / 0.013=?

    • Options
    • A. .13
    • B. .013
    • C. 1.3
    • D. 13
    • Discuss
    • 2. 
      Two posts are x meter apart and the height of one is double that of the other. If from the midpoint of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meter) of the shorter post is :

    • Options
    • A. x 2 ?2
    • B. x 4
    • C. x ?2
    • D. x ?2
    • Discuss
    • 3. 
      If p/q =4/5, then the value of 4/7 + {(2q - p) / (2q + p)} is?

    • Options
    • A. 3 / 7
    • B. 34
    • C. 1
    • D. 2
    • Discuss
    • 4. 
      What is 25% of 25% is equal to?

    • Options
    • A. 6.25
    • B. .625
    • C. .0625
    • D. .000625
    • Discuss
    • 5. 
      The number .05 is hoe many percent of 20?

    • Options
    • A. 25
    • B. .025
    • C. .25
    • D. 2.5
    • Discuss
    • 6. Find the lowest common multiple of 24, 36 and 40.

    • Options
    • A. 120
    • B. 240
    • C. 360
    • D. 480
    • Discuss
    • 7. 
      8 1/ 3% expressed as a fraction is?

    • Options
    • A. 25/3
    • B. 3/25
    • C. 1/12
    • D. 1/4
    • Discuss
    • 8. 
      .025 in terms of term of rate per cent is?

    • Options
    • A. .25%
    • B. 2.5%
    • C. 0.25%
    • D. 371/2%
    • Discuss
    • 9. 
      What percentage of 2/7 is 1/35?

    • Options
    • A. 2.5%
    • B. 10%
    • C. 25%
    • D. 20%
    • Discuss
    • 10. 
      A sum of ? 4000 is lent out in two parts, one at 8% simple interest and other at 10% simple interest. If the annual interest is ? 352, the sum lent at 8% is

    • Options
    • A. ? 1600
    • B. ? 2400
    • C. ? 1800
    • D. ? 2800
    • Discuss


    Comments

    There are no comments.

Enter a new Comment