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GMAT Practice - Permutation & Probability

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You may get two to three questions from Permutation Combination, counting methods and probability in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include selecting one or more objects from a sample space, reordering objects with or without a constraint, questions on number sequences, tossing of coins, rolling a die, picking cards from a pack of cards, conditional probability, probability of exhaustive events, complimentary events, mutually exclusive events and independent events. A collection of GMAT practice questions from counting methods and discrete probability is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

    1. 6! / 2!
    2. 3! * 3!
    3. 4! / 2!
    4. (4! * 3!) / 2!
    5. (3! * 3!) / 2!
    • Correct AnswerChoice (D).
      The number of rearrangements of ABACUS in which the vowels always appear together is
      (4! * 3!) / 2!
      Correct answer
    • Explanatory Answer
    • Reordering Letters
    • Easy
  2. How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

    1. 59
    2. 11! / (2!*2!*2!)
    3. 56
    4. 23
    5. 11! / (3!*2!*2!*2!)
    • Correct AnswerChoice (A).
      The number of reorderings in which the first letter is E and the last one is R is 59.
      Correct answer
    • Explanatory Answer
    • Rearranging Letters
    • Easy
  3. What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?

    1. 1/4
    2. 1/6
    3. 1/3
    4. 1/24
    5. 1/12
    • Correct AnswerChoice (A).
      The probability that the positions of the consonants remain unchanged is 1/4.
      Correct answer
    • Explanatory Answer
    • Reaaranging Letters
    • Easy
  4. There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

    1. 5
    2. 21
    3. 33
    4. 60
    5. 6
    • Correct AnswerChoice (B).
      The required number of ways to achieve the stated condition is 21.
      Correct answer
    • Explanatory Answer
    • Counting Methods
    • Medium
  5. A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?

    1. 1
    2. 1/256
    3. 81/256
    4. 175/256
    5. 144/256
    • Correct AnswerChoice (D).
      The probability that he will hit the target is
      175/256
      Correct answer
    • Explanatory Answer
    • Probability : Exhaustive Events
    • Medium
  6. In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

    1. 5 C 3
    2. 5 P 3
    3. 53
    4. 35
    5. 25
    • Correct AnswerChoice (D).
      The number of ways of posting the 5 letters in the 3 boxes is 35.
      Correct answer
    • Explanatory Answer
    • Sampling with replacement
    • Medium
  7. Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

    1. 210
    2. 29
    3. 3 * 28
    4. 3 * 29
    5. None of these
    • Correct AnswerChoice (B).
      The number of outcomes in which the 3rd coin will turn up heads is 29.
      Correct answer
    • Explanatory Answer
    • Tossing Coins
    • Medium
  8. In how many ways can the letters of the word "PROBLEM" be rearranged to make seven letter words such that none of the letters repeat?

    1. 7!
    2. 7C7
    3. 77
    4. 49
    5. None of these
    • Correct AnswerChoice (A).
      The number of rearrangements of the word PROBLEM is 7!.
      Correct answer
    • Explanatory Answer
    • Rearranging Letters
    • Easy
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