GMAT Quant Probability

Practice Questions in Permutation

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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. 3! * 3!
    2. \\frac{4!}{2!})
    3. \\frac{4! * 3!}{2!})
    4. \\frac{3! * 3!}{2!})
  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. \\frac{11!}{2! * 2! * 2!})
    3. 56
    4. 23
    5. \\frac{11!}{3!*2!*2!*2!})
  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. \\frac{1}{4})
    2. \\frac{1}{6})
    3. \\frac{1}{3})
    4. \\frac{1}{24})
    5. \\frac{1}{12})
  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
  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. \\frac{1}{256})
    3. \\frac{81}{256})
    4. \\frac{175}{256})
    5. \\frac{144}{256})
  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
  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
  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
  9. Bag x contains 3 red and 5 black balls and bag y contains 4 red and 4 black balls. One bag is selected at random and from the selected bag one ball is drawn. What is the probability that the ball drawn is red?

    1. \\frac{7}{8})
    2. \\frac{7}{16})
    3. \\frac{3}{16})
    4. \\frac{4}{5})
    5. \\frac{9}{16})

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