Solved Examples: Permutations and Combinations

# Solved Examples: Permutations and Combinations Video Lecture | Quantitative Aptitude for SSC CGL

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

## FAQs on Solved Examples: Permutations and Combinations Video Lecture - Quantitative Aptitude for SSC CGL

 1. What is the difference between permutations and combinations?
Ans. Permutations and combinations are both ways of counting the number of possible outcomes in a given scenario. The main difference lies in whether the order of the elements matters. In permutations, the order matters, while in combinations, the order does not matter. For example, when arranging a group of people in a line, the order in which they stand is important, so it is a permutation. On the other hand, if we are selecting a group of people to form a committee, the order in which they are selected does not matter, so it is a combination.
 2. How do I calculate permutations?
Ans. To calculate permutations, you need to determine the number of ways to arrange a set of objects in a specific order. The formula for calculating permutations is nPr = n! / (n - r)!, where n represents the total number of objects, and r represents the number of objects being arranged in a specific order. The exclamation mark denotes the factorial function, which means multiplying a number by all the positive integers less than it. For example, if you have 5 objects and want to arrange 3 of them, the permutation would be 5P3 = 5! / (5 - 3)! = 5! / 2! = 60.
 3. How do I calculate combinations?
Ans. Combinations are used to calculate the number of ways to select objects from a set without regard to their order. The formula for calculating combinations is nCr = n! / (r!(n - r)!), where n represents the total number of objects, and r represents the number of objects being selected. Again, the exclamation mark denotes the factorial function. For example, if you have 5 objects and want to select 3 of them, the combination would be 5C3 = 5! / (3!(5 - 3)!) = 5! / (3!2!) = 10.
 4. Can permutations and combinations be applied in real-life situations?
Ans. Yes, permutations and combinations have numerous applications in real-life situations. For example, when scheduling events, you may need to consider various permutations of time slots and activities. In sports, the order in which teams are placed in a tournament bracket can be calculated using permutations. Combinations are used in probability theory to calculate the likelihood of drawing specific cards from a deck or winning in a lottery. These concepts are also used in computer science, cryptography, and data analysis.
 5. Are there any shortcuts or tricks to solve permutations and combinations problems?
Ans. While there may not be shortcuts to solve all permutations and combinations problems, there are certain techniques that can simplify calculations. For example, if there are identical objects in a set, you can divide the total number of permutations or combinations by the factorial of the number of identical objects to avoid overcounting. Additionally, understanding the concept of symmetry can help reduce the number of cases to consider. Practice and familiarity with the formulas and concepts can also speed up problem-solving.

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

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