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  • Question
  • How many number of times will the digit ?7' be written when listing the integers from 1 to 1000?


  • Options
  • A. 243
  • B. 300
  • C. 301
  • D. 290

  • Correct Answer
  • 300 

    Explanation

    7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.

     

    1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc

     

    This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)

     

    You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.

     

    In each of these numbers, 7 is written once. Therefore, 243 times.

     

     

    2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77

     

    In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).

     

    There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.

     

    In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.

     

     

    3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.

     

    Therefore, the total number of times the digit 7 is written between 1 and 999 is

     

    243 + 54 + 3 = 300


  • Permutation and Combination problems


    Search Results


    • 1. A certain marathon had 50 people running for first prize, second, and third prize.How many ways are there to correctly guess the first, second, and third place winners?

    • Options
    • A. 2
    • B. 1
    • C. 4
    • D. 3
    • Discuss
    • 2. Find the number of ways to draw a straight, (suit does not matter) beginning with a 4 and ending with a 8?

    • Options
    • A. 1024
    • B. 1296
    • C. 1094
    • D. 1200
    • Discuss
    • 3. A school has scheduled three volleyball games, two soccer games, and four basketball games. You have a ticket allowing you to attend three of the games. In how many ways can you go to two basketball games and one of the other events?

    • Options
    • A. 25
    • B. 30
    • C. 50
    • D. 75
    • Discuss
    • 4. Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

    • Options
    • A. 2589860
    • B. 2598970
    • C. 2598960
    • D. 2430803
    • Discuss
    • 5. How many ways are there to select a subcommittee of 7 members from among a committee of 17?

    • Options
    • A. 19000
    • B. 19448
    • C. 19821
    • D. 19340
    • Discuss
    • 6. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

    • Options
    • A. 126
    • B. 240
    • C. 120
    • D. 260
    • Discuss
    • 7. Eight first class and six second class petty officers are on the board of the 56 club. In how many ways can the members elect, from the board, a president, a vice-president, a secretary, and a treasurer if the president and secretary must be first class petty officers and the vice-president and treasurer must be second class petty officers?

    • Options
    • A. 1500
    • B. 1860
    • C. 1680
    • D. 1640
    • Discuss
    • 8. There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

    • Options
    • A. 18! x 19!
    • B. 2 x 19!
    • C. 2 x 18!
    • D. 18! x 18!
    • Discuss
    • 9. In how many ways can the letters of the word 'MISSISIPPI' be arranged ?

    • Options
    • A. 12400
    • B. 11160
    • C. 16200
    • D. 12600
    • Discuss
    • 10. In how many ways, can zero or more letters be selected form the letters AAAAA?

    • Options
    • A. 5
    • B. 6
    • C. 2
    • D. 8
    • Discuss


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