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  • Question
  • Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.


  • Options
  • A. 105555
  • B. 106665
  • C. 106656
  • D. 108333

  • Correct Answer
  • 106656 

    Explanation

    The number of arrangements of 4 different digits taken 4 at a time is given by  4 P 4  = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands.

     

     

     

    Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places.

     

     

     

    Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656


  • Permutation and Combination problems


    Search Results


    • 1. Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?

    • Options
    • A. 360
    • B. 780
    • C. 720
    • D. 240
    • Discuss
    • 2. A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours. Which of the following is/are correct ?

    • Options
    • A. F is third to the left of B
    • B. F is second to the right of B
    • C. B is an immediate neighbour of D
    • D. All of the above
    • Discuss
    • 3. How many such pair of letters are there in the word ?TROUBLED? which have as many letters between them in the word as they have between them in the English alphabet?

    • Options
    • A. 2
    • B. 3
    • C. 4
    • D. 5
    • Discuss
    • 4. What is the value of 100P2 ?

    • Options
    • A. 10000
    • B. 9900
    • C. 8900
    • D. 7900
    • Discuss
    • 5. In how many different ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together?

    • Options
    • A. 112420
    • B. 85120
    • C. 40320
    • D. 1209600
    • Discuss
    • 6. If repetition of the digits is allowed, then the number of even natural numbers having three digits is :

    • Options
    • A. 550
    • B. 450
    • C. 500
    • D. 540
    • Discuss
    • 7. In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?

    • Options
    • A. 1440
    • B. 720
    • C. 2250
    • D. 3600
    • Discuss
    • 8. In how many ways the letters of the word NUMERICAL can be arranged so that the consonants always occupy the even places ?

    • Options
    • A. 5!
    • B. 6!
    • C. 4!
    • D. Can't determine
    • Discuss
    • 9. 5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

    • Options
    • A. 2880
    • B. 1440
    • C. 720
    • D. 2020
    • Discuss
    • 10. In how many ways can 5 letters be posted in 4 letter boxes?

    • Options
    • A. 512
    • B. 1024
    • C. 625
    • D. 20
    • Discuss


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