- Permutations and Combinations Problems | GMAT GRE Maths Tutorial | MBA Crystal Ball
- Combinations vs Permutations
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So that gives us a total of 11 for the silver medal spot. Finally, that leaves us with 10 athletes for the bronze medal podium. You might notice that this is the fundamental counting principle. The idea that when we are looking for total number of outcomes, we multiply numbers—or in this case, the number that goes on top of each dash—together.

To give you an idea of how a combinations can show up along with the fundamental counting principle, try the following question:. Pearson has 4 boys and 5 girls in her class. She is to choose 2 boys and 2 girls to serve on her grading committee. If one girl and one boy leave before she can make a selection, then how many unique committees can result from the information above?

The first step in this problem is recognizing whether we are dealing with combinations or permutations.

That is, either you are in the committee or out of the committee there are no gold medalists here! The next thing to notice with this problem is that of the original 9 students, 2 leave, one boy and one girl. So that leaves us with 3 boys and 4 girls. We want to choose two each. Therefore, we have to set up one combination for boys and one for girls. For boys, we have 3C2 and for girls we have 4C2. How many different shirt-pants getups can you wear? Well, for each shirt there are 3 options of pants.

Therefore, we multiply and get 9.

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Even if you miss a question—likely because it is very difficult—the fundamentals in this post should be enough to help you understand the explanation to that question, so that you can get a similar question right in the future. And many many many problems. Who this course is for:. Course content. Expand all 14 lectures Fundamental Principle of Counting If we want to do counting in a better way, we have to learn science behind counting.

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Two fundamental principles of counting are the Addition Principle, Multiplication Principle. All subsequent concepts, here will build upon these two principles. Introducing Fundamental Theory of Counting.

Preview Fundamental theory of counting- Multiplication Principle. Problems on Fundamental Theory of Counting. Quiz on Fundamental theory of counting. Arrangement of objects: Permutation formula. Selection of Objects: Combination.

## Permutations and Combinations Problems | GMAT GRE Maths Tutorial | MBA Crystal Ball

Permutation We have seen in example of factorials that we need the same number of students as chairs to sit on. Let us start again by listing all possibilities: To find a simple formula like the one above, we can think about it in a very similar way.

Problems on Selection and arrangements. Practice test of Selection and arrangements of objects previous two lectures. Selection and arrangements of objects. Arrangements of objects in a circular Table: Circular Permutation. Problems on Circular arrangements.

## Combinations vs Permutations

Practice problems on Arrangement of objects in circular table. Arrangement of objects in circular table. How many ways can we award a 1st, 2nd and 3rd place prize among eight contestants? We had to order 3 people out of 8. To do this, we started with all options 8 then took them away one at a time 7, then 6 until we ran out of medals. Unfortunately, that does too much! And why did we use the number 5? Because it was left over after we picked 3 medals from 8.

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So, a better way to write this would be:. If we have n items total and want to pick k in a certain order, we get:. And this is the fancy permutation formula: You have n items and want to find the number of ways k items can be ordered:.