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Counting: Permutations & Combinations Video Lecture | CSAT Preparation - UPSC

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FAQs on Counting: Permutations & Combinations Video Lecture - CSAT Preparation - UPSC

1. What is the difference between permutations and combinations in counting?
Ans. Permutations and combinations are both counting techniques used in mathematics. The main difference between them lies in the order in which the objects are arranged. In permutations, the order matters, while in combinations, the order does not matter.
2. How do I calculate the number of permutations?
Ans. To calculate the number of permutations, you need to multiply the total number of objects by the number of choices for each object. For example, if you have 5 objects and you want to arrange them in a specific order, you would have 5 choices for the first object, 4 choices for the second object, 3 choices for the third object, and so on. The total number of permutations would be 5 x 4 x 3 x ... (until you have used all the objects).
3. How do I calculate the number of combinations?
Ans. To calculate the number of combinations, you need to use the formula nCr, where n is the total number of objects and r is the number of objects you choose at a time. The formula for combinations is n! / (r! * (n-r)!), where ! represents factorial. For example, if you have 5 objects and you want to choose 3 of them without considering the order, the number of combinations would be 5! / (3! * (5-3)!).
4. Can you provide an example of permutations and combinations in real-life scenarios?
Ans. Sure! Let's consider a scenario where you have 6 friends and you want to form a committee of 3 people. - If the order in which your friends are chosen matters (permutations), then the number of possibilities would be 6P3 = 6! / (6-3)! = 6! / 3! = 120. - If the order doesn't matter (combinations), then the number of possibilities would be 6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = 20.
5. How are permutations and combinations used in probability?
Ans. Permutations and combinations are fundamental concepts in probability. They are used to calculate the probability of events occurring in different scenarios. For example, if you want to find the probability of drawing a specific hand in a game of poker, you would use combinations. If you want to find the probability of a specific sequence of events, such as the outcome of a coin toss followed by a dice roll, you would use permutations. These counting techniques help in understanding the likelihood of different outcomes in probability problems.
207 videos|156 docs|192 tests
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