# GRE® Permutation & Probability

Free GRE Quant Practice Questions

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### Concepts Tested in Permutation Combination

One can expect two to three questions from permutation combination and counting methods. It is imperative that you understand the basics of permutation and combination well so that you will be able to tackle questions from this topic. The following concepts are tested in permutation and combination in the GRE test.

• Sampling with and without replacement
• Sampling where order matters and where order does not matter
• Difference between permutation and combination
• Number sequence examples in counting methods
• Re ordering letters of a word
• Tossing of coins, rolling dice and pack of cards

### Concepts Tested in Probability

If you have understood the basics of permutation and combination well, solving questions from probability becomes easy. In fact, many probability questions are a set of two permutation probability questions with the denominator being the total number of outcomes for an event and the numerator being the number of favorable outcomes. The following concepts are tested.

• Computing probabilities for events that are equally likely
• Computing probabilities for independent events that occur together
• Mutually exclusive events
• Conditional probabilities
• Geometric probabilities
1. There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

1. 10
2. 9
3. 20
4. 625
5. 1024
2. In how many ways can 3 students be selected from a group of 12 students to represent a school in the inter school essay competition?

1. 10
2. 9
3. 20
4. 625
5. 1024
3. How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)

1. $$frac{8!}{2!}$ 2. 8! - 2! 3. 6! 4. 8! - 2 * 7! 5. 6! * 2! 4. GRE Quantitative Comparison Question Quantity A Quantity B The probability that a word selected from the set of all rearrangements of the letters of the word "Math" results in "Math" The probability that a word selected from the set of all rearrangements of the letters of the word "Good" results in "Good" 1. Quantity A is greater 2. Quantity B is greater 3. The two quantities are equal 4. The relationship cannot be determined from the information given 5. In how many rearrangements of the letters of the word SCINTILLATING will no two 'I's appear together? 1. 11C3 * 13! 2. $\frac{10!}{2! * 2! * 2!}$ 3. 11C3 * 3! * 10! 4. 11C3 $\frac{10!}{2! * 2! * 2!}$ 5. $\frac{11!}{2! x 2! x 2!}$ 6. How many squares are there in a chess board? 1. 64 2. 65 3. 4096 4. 1296 5. 204 7. What is the probability that two squares$smallest dimension) selected randomly from a chess board will have only one common corner?

1. $\frac{7}{288}$
2. $\frac{7}{144}$
3. $\frac{7}{126}$
4. $\frac{7}{72}$
5. $\frac{2}{63}$
8. 8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated?

1. 9!
2. 7! * 2
3. 9! * 2
4. 8! * 2
5. 8!
9. Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire day then

1. 0.25 ≤ P ≤ 0.35
2. 0.25 ≤ P ≤ 0.65
3. 0.4 ≤ P ≤ 0.65
4. 0.35 ≤ P ≤ 0.4
5. 0.1 ≤ P ≤ 0.6
10. For which of the following events will the number of outcomes exceed 50?
Indicate all such events.

1. The number of outcomes in which at least three heads appears in 6 consecutive tosses of a fair coin.
2. The number of outcomes in which the sum of the digits that appear on the facing side is odd when a fair die rolled thrice.
3. The number of outcomes in which the two cards drawn from a pack of well shuffled cards are both red and face cards.
4. The number of outcomes in which the vowels appear together when the letters of the word 'PRIORITY' are reordered.
5. The number of ways of posting 6 different letters in 2 different post boxes such that at least one letter is posted in each of the boxes.
6. The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising 3 Indians and 4 Americans and no one else.