53 people are sitting in a hall. 14 mc
How many people are sitting in the
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Make number cards from 1 to 48
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GMAT Club Forum Index Quantitative
Combinatorics Made Easy! : Quantitative
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Bunuel
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Updated on: Feb 4, 2019
Combinatorics Made Easy!
CONTENT
1. Permutation and Combination Basics
2. The Dreaded Combinatorics
3. Circular Arrangements
4. Linear Arrangement Constraints - Part I
5. Linear Arrangement Constraints - Part II
6. Circular Arrangement Constraints - Part I
7. Circular Arrangement Constraints – Part II
8. Considering Combinations
9. Combinations with Constraints
10. Using Combinations to Make Groups
11. Tackling the Beasts Together
12. Unfair Distributions in Combinatorics - Part I
13. Unfair Distributions in Combinatorics - Part II
14. How to Solve Combinatorics Questions on the GMAT
15. When Permutations & Combinations and Data Sufficiency Come Together on the GMAT!
16. Other Resources on Combinatorics
17. Should You Use the Permutation or Combination Formula?
18. Permutation Involving Sum of Digits
19. Easy Logic to a Difficult Combinatorics GMAT Question!
Permutation and Combination Basics
BY Vivian Kerr, VERITAS PREP
Aiming for a 700+ on the GMAT? You never know when a challenging combination or permutation question will pop up three-quarters of the way through your exam to wreck havoc on your score. This advanced concept is not as commonly tested as algebra fundamentals or number properties, but it’s definitely worth knowing the basics in case you do see it.
The Fundamental Counting Principle states that if an event has x possible outcomes and a different independent event has y possible outcomes, then there are xy possible ways the two events could occur together. For example, how many three-digit integers have either 6 or 9 in the tens digit and 1 in the units digit?
To solve, we need to find the possible outcomes for each digit (hundreds, tens, and units) and multiply them. Each digit has 10 possible values (0 through 9). The hundreds digit can be any of these except 0 (since a three-digit number cannot begin with 0). The tens digit has only 2 options (6 or 9). The units digit has only 1 possibility (1). Therefore, the total number of possibilities is 9 x 2 x 1 = 18.
Permutations are sequences. In a sequence, order is important. How many different ways can four people sit on a bench? For the first spot on the bench, we have 4 to choose from. For the next spot we’ll have 3, for the third spot we’ll have 2, and the last remaining person will take the final spot. Therefore, there are 4 x 3 x 2 x 1 = 24 ways. Harder permutations problems will require you to use this formula:
n = the number of options
r = the number chosen from those options
For example, how many possible options are there for the gold, silver, and bronze medals out of 12 athletes? Here n = 12 and r = 3. Since the order in which the athletes finish matters, we know to use the Permutation formula:
options
Combinations are groups. Order doesn’t matter. The Combination formula is only slightly different from the Permutation formula: