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Home Aptitude Permutation and Combination Comments

  • Question
  • How many numbers can be formed from 1, 2, 3, 4, 5, ( without repetition), when the digit at the unit's place must be greater than that in the ten's place?


  • Options
  • A. 54
  • B. 60
  • C. 51/3
  • D. 2 x 4!

  • Correct Answer
  • 60 

    Explanation

    The digit in the unit's place should be greater than that in the tens' place.
    Hence, if digit 5 occupies the unit place, then remaining four digits need not to follow any order,hence required number = 4!
    However, if digit 4 occupies the unit place then 5 cannot occupy the ten;s position. Hence, digit at the ten's place and it will be filled by the digit 1, 2 or 3. This can happen in 3 ways. The remaining 3 digit can be filled in the remaining three place in 3! ways.
    Hence, in all, we have (3 x 3!) numbers ending in 4. Similarly, if we have 3 in the unit's place and it will be either 1 or 2. this can happen in 2 ways. Hence, we will have (2 x 3! ) number ending in 3 . Similarly, we can find that there will be 3! numbers ending in 2 and no number with 1. Hence, total number of numbers
    = 4! + (3) x 3! + (2 x 3!) + 3!
    = 4! + 6 x 3! = 24 + (6 x 6) = 60


  • Permutation and Combination problems


    Search Results


    • 1. 
      An intelligence agency forms a code of two distinct digits selected from 0, 1, 2,....., 9 such that the first-digit of code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down, for examples the code 91 may appear as 16. how many codes are there for which no such confusion can arise?

    • Options
    • A. 80
    • B. 78
    • C. 71
    • D. 69
    • Discuss
    • 2. 
      A new flag is to be designed with six vertical stripes using some or all of the colour yellow, green,blue and red. Then, the number of ways this can be made such that no two adjacent stripes have the same colour is

    • Options
    • A. 12 x 81
    • B. 16 x 192
    • C. 20 x 125
    • D. 24 x 216
    • Discuss
    • 3. 
      A five-digit number divisible by 3 is to be formed using digits 0, 1, 2, 3, 4 and 5 without repetition, the total number of ways this can be done, is

    • Options
    • A. 122
    • B. 210
    • C. 216
    • D. 217
    • Discuss
    • 4. 
      The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a group consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is

    • Options
    • A. 1960
    • B. 3240
    • C. 1540
    • D. None of these
    • Discuss
    • 5. 
      There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities, is

    • Options
    • A. 92
    • B. 90
    • C. 91
    • D. 93
    • Discuss
    • 6. 
      Boxes numbered 1, 2, 3, 4, and 5 are kept in a row and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

    • Options
    • A. 8
    • B. 10
    • C. 15
    • D. 22
    • Discuss
    • 7. 
      Marks obtained by an student in 5 subjects are given below 25, 26, 27, 28, 29 in these obtained marks 27 is

    • Options
    • A. mode
    • B. median and mode
    • C. mean and median
    • D. both (a) and (c)
    • Discuss
    • 8. 
      The median for the data 2, 4, 6, 8, 10, 12, 14 is

    • Options
    • A. 6
    • B. 8
    • C. 9.5
    • D. 10
    • Discuss
    • 9. 
      Reaching the place of meeting on Tuesday 15 min before 8:30 h, Anuj found himself half an hour earlier than the man who was 40 min late. What was the scheduled time of the meeting?

    • Options
    • A. 8:00 h
    • B. 8:05 h
    • C. 8:15 h
    • D. 8:45 h
    • Discuss
    • 10. 
      A clock buzzes 1 time at 1 O'clock, 2 time at 2 O'clock, 3 times at 3 O'clock and so on. What will be the total number of buzzes in a day?

    • Options
    • A. 150
    • B. 156
    • C. 100
    • D. None of these
    • Discuss


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