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  • Question
  • The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :


  • Options
  • A. 100
  • B. 200
  • C. 300
  • D. 400

  • Correct Answer
  • 300 

    Explanation

     Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where  0 ? x , y , z ? 9 .

     

    Let us first count the numbers in which 8 occurs exactly once.

     

    Since 8 can occur atone place in  3 C 1 ways. There are  3   x   9   x   9    such numbers.

     

    Next, 8 can occur in exactly two places in  3 C 2 × 9  such numbers. Lastly, 8 can occur in all three digits in one number only.

      

    Hence, the number of times 8 occur is 

      1 × 3 × 9 2 + 2 × 3 × 9 + 3 × 1   =   300


  • Permutation and Combination problems


    Search Results


    • 1. A Group consists of 4 couples in which each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?

    • Options
    • A. 1152
    • B. 1278
    • C. 1296
    • D. None of these
    • Discuss
    • 2. A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?

    • Options
    • A. 3
    • B. 5
    • C. 3!
    • D. 5!
    • Discuss
    • 3. When John arrives in New York,he has eight stops to see, but he has time only to visit six of them.In how many different ways can he arrange his schedule in New York?

    • Options
    • A. 20610
    • B. 24000
    • C. 20160
    • D. 21000
    • Discuss
    • 4. First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?

    • Options
    • A. 1736
    • B. 1716
    • C. 1216
    • D. 1346
    • Discuss
    • 5. In how many different ways can five persons stand in a line for a group photograph?

    • Options
    • A. 120
    • B. 240
    • C. 360
    • D. 720
    • Discuss
    • 6. There are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made ?

    • Options
    • A. 49450
    • B. 50540
    • C. 46587
    • D. 52487
    • Discuss
    • 7. How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ?

    • Options
    • A. 59
    • B. 60
    • C. 61
    • D. 64
    • Discuss
    • 8. If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ?X? as the answer. If no such word can be formed, give ?Z? as the answer.

    • Options
    • A. T
    • B. X
    • C. N
    • D. R
    • Discuss
    • 9. In the below word how many words are there in which R and W are at the end positions? RAINBOW

    • Options
    • A. 120
    • B. 180
    • C. 210
    • D. 240
    • Discuss
    • 10. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

    • Options
    • A. 1260
    • B. 210
    • C. 210 x 6!
    • D. 1512
    • Discuss


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