Grade 11 Exam > Grade 11 Videos > Mathematics for Grade 11 > Examples of Combinations (NCERT) - Permutations and Combinations
Examples of Combinations (NCERT) - Permutations and Combinations Video Lecture | Mathematics for Grade 11
FAQs on Examples of Combinations (NCERT) - Permutations and Combinations Video Lecture - Mathematics for Grade 11
| 1. What is the difference between permutations and combinations? |  |
Ans. Permutations and combinations are both counting principles used in mathematics. The main difference between the two is that permutations take into account the order of the elements, whereas combinations do not consider the order. In permutations, the arrangement matters, whereas in combinations, the arrangement does not matter.
| 2. How do you calculate the number of combinations? | |
Ans. To calculate the number of combinations, we use the formula C(n, r) = n! / (r! * (n-r)!), where n is the total number of objects, and r is the number of objects chosen at a time. The exclamation mark (!) represents the factorial operation, which is the product of all positive integers less than or equal to the given number.
| 3. Can you provide an example of a combination problem? | |
Ans. Sure! Let's say you have 5 different books on a shelf, and you want to choose 3 books to take on a trip. In this case, you are looking for the number of combinations. Using the formula C(5, 3) = 5! / (3! * (5-3)!), the number of combinations is 10. Therefore, there are 10 different ways to choose 3 books out of 5.
| 4. What is the significance of combinations in real-life scenarios? | |
Ans. Combinations have various applications in real-life scenarios. For example, when creating a password using a combination lock, the number of possible combinations determines the level of security. In sports, combinations are used to determine the number of possible outcomes in a tournament or match. Combinations are also utilized in probability and statistics to calculate the likelihood of events occurring.
| 5. How do permutations and combinations relate to each other? | |
Ans. Permutations and combinations are closely related concepts. Combinations are derived from permutations by eliminating the cases where the order matters. In other words, combinations are a subset of permutations. By understanding permutations, we can derive the formula for combinations and vice versa. The relationship between the two concepts allows us to solve a wide range of counting problems efficiently.
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