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  • Question
  • Three dice (each having six faces with each face having one number from 1 or 6 ) are rolled. What is the number of possible outcomes such that atleast one dice shows the numbers 2?


  • Options
  • A. 36
  • B. 81
  • C. 91
  • D. 116

  • Correct Answer
  • 91 

    Explanation

    When three dice are rolled, the number of possible outcomes = 63 = 216
    Number of possible outcomes in which 2 does not appear on any dice = 53 = 125
    ? Number of possible outcomes in which atleast one dice shows 2 = 216 - 125 = 91


  • Permutation and Combination problems


    Search Results


    • 1. 
      A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is?

    • Options
    • A. 7
    • B. 8
    • C. 9
    • D. 24
    • Discuss
    • 2. 
      In how many difference ways can six players be arranged in a line such that two of them, Abhinav and Manjesh are never together?

    • Options
    • A. 120
    • B. 240
    • C. 360
    • D. 480
    • Discuss
    • 3. 
      In a question paper, there are four multiple choice type question. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

    • Options
    • A. 19
    • B. 120
    • C. 624
    • D. 1024
    • Discuss
    • 4. 
      Groups, each containing 3 boys are to be formed out of 5 boys, A, B , C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?

    • Options
    • A. 5
    • B. 6
    • C. 7
    • D. 8
    • Discuss
    • 5. 
      A question paper had 10 questions. Each question could only be answered as True (T) or false (F). Each candidate answered all the questions. Yet, no two candidate wrote the answers in an identical sequence. How many different sequences of answers are possible?

    • Options
    • A. 20
    • B. 40
    • C. 512
    • D. 1024
    • Discuss
    • 6. 
      How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed?

    • Options
    • A. 3125
    • B. 625
    • C. 3905
    • D. 125
    • Discuss
    • 7. 
      Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat?

    • Options
    • A. 4!
    • B. 8!
    • C. 6!
    • D. 9!
    • Discuss
    • 8. 
      2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the five seats be occupied by these passengers?

    • Options
    • A. 15
    • B. 36
    • C. 48
    • D. 60
    • Discuss
    • 9. 
      139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round without actually playing in the first round. The pairing continues on the next round with a bye to any player left over. If the schedule is planned, so that a minimum number of matches is required to determine the champion, the number of matches which must be played is?

    • Options
    • A. 136
    • B. 137
    • C. 138
    • D. 139
    • Discuss
    • 10. 
      In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways can the three questions be selected?

    • Options
    • A. 1944
    • B. 2094
    • C. 1894
    • D. 2194
    • Discuss


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