CA Foundation Exam > CA Foundation Videos > Quantitative Aptitude for CA Foundation > Permutations & Combinations- 1
Permutations & Combinations- 1 Video Lecture | Quantitative Aptitude for CA Foundation
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FAQs on Permutations & Combinations- 1 Video Lecture - Quantitative Aptitude for CA Foundation
| 1. What is the difference between permutations and combinations? |  |
Ans. Permutations and combinations are both concepts in mathematics that involve counting and arranging objects. The main difference between the two is that permutations take into account the order or arrangement of the objects, while combinations do not consider the order. In permutations, the order of the objects matters, whereas in combinations, the order does not matter.
| 2. How do you calculate permutations? | |
Ans. To calculate permutations, you can use the formula P(n, r) = n! / (n - r)!, where n represents the total number of objects and r represents the number of objects being selected or arranged. The exclamation mark represents the factorial function, which means multiplying a number by all the positive integers less than itself. For example, if you have 5 objects and want to arrange them in groups of 3, the permutation would be P(5, 3) = 5! / (5 - 3)! = 5! / 2! = 60.
| 3. How do you calculate combinations? | |
Ans. To calculate combinations, you can use the formula C(n, r) = n! / (r! * (n - r)!), where n represents the total number of objects and r represents the number of objects being selected without considering the order. Similar to permutations, the exclamation mark represents the factorial function. For example, if you have 5 objects and want to select 3 of them without considering the order, the combination would be C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = 10.
| 4. Can permutations and combinations be applied to real-life situations? | |
Ans. Yes, permutations and combinations are widely used in real-life situations. For example, in probability theory, permutations and combinations are used to calculate the number of possible outcomes in an event. In sports, permutations and combinations are used to determine the number of possible match outcomes or team formations. In computer science, permutations and combinations are used in algorithms and data structures. Overall, permutations and combinations have various applications in different fields.
| 5. Are there any shortcuts or tricks to solve permutations and combinations problems? | |
Ans. Yes, there are certain shortcuts or tricks that can be used to solve permutations and combinations problems more efficiently. For example, the concept of factorial can be simplified by canceling common factors. Additionally, the concept of combinations can be simplified by using the property C(n, r) = C(n, n - r), which states that the number of combinations selecting r objects from a set of n objects is equal to the number of combinations selecting n - r objects from the same set. These shortcuts and tricks can save time and effort in solving permutations and combinations problems.
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