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Home Aptitude Permutation and Combination See What Others Are Saying!
  • Question
  • What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?


  • Options
  • A. 28450
  • B. 26340
  • C. 32640
  • D. 36450

  • Correct Answer
  • 32640 

    Explanation

    We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

     

    The formula to find sum of all numbers in a permutation is

     

    111 x no of ways numbers can be formed for a number at given position x sum of all given digits

     

    No of 1 s depends on number of digits

     

    So,the answer us

     

    111 x 20 x (0+1+2+3+4+5) = 33300

     

    We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

     

    Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

     

    This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

     

    So the sum for this is 11 x 4 x (1+2+3+4+5).
    =660

     

    Hope u understood why we use 4. Each number can be formed in 4x1 ways

     

    So, the final answer is 33300-660 = 32640

  • Tags: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk

    More questions

    • 1. 
      A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is?

    • Options
    • A. 4:1
    • B. 1.4
    • C. 2:1
    • D. 1:2
    • Discuss
    • 2. 
      The length of the train that takes 8 second to pass a pole where it runs at a speed of 36 km/hr is?

    • Options
    • A. 288 meters
    • B. 45 meters
    • C. 48 meters
    • D. 80 meters
    • Discuss
    • 3. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 4. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

    • Options
    • A. 3.6 sec
    • B. 18 sec
    • C. 36 sec
    • D. 72 sec
    • Discuss
    • 5. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

    • Options
    • A. 48 km/hr
    • B. 54 km/hr
    • C. 66 km/hr
    • D. 82 km/hr
    • Discuss
    • 6. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

    • Options
    • A. 9 a.m.
    • B. 10 a.m.
    • C. 10.30 a.m.
    • D. 11 a.m.
    • Discuss
    • 7. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 8. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

    • Options
    • A. Rs. 21,000
    • B. Rs. 22,500
    • C. Rs. 25,300
    • D. Rs. 25,800
    • Discuss
    • 9. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

    • Options
    • A. 2 or 6
    • B. 4
    • C. 4 or 8
    • D. 8
    • E. None of these
    • Discuss
    • 10. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?

    • Options
    • A. 3
    • B. 6
    • C. 7
    • D. 8
    • Discuss


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