Jawahar Navodaya Vidyalaya Selection Test (JNVST)
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Arrangements: Arranging items in a specific order based on given conditions
🚀 Arranging items in a specific order based on given conditions is a common problem-solving task. Imagine you are organizing a bookshelf with different books, and you want to arrange them by size, color, or author. Similarly, in math, we often need to arrange numbers, objects, or people based on certain rules or conditions. This concept is crucial for developing logical thinking and problem-solving skills, especially for exams like the JNVST.
Examples💡
Example 1: Suppose you have 3 friends: Anil, Bina, and Chitra. You want to arrange them in a line for a photo. How many different ways can you arrange them? Solution: You can arrange them in 3! (3 factorial) ways, which is 3 x 2 x 1 = 6 ways.
Example 2: You have 4 different colored marbles: red, blue, green, and yellow. You want to arrange them in a row. How many different arrangements are possible? Solution: You can arrange them in 4! (4 factorial) ways, which is 4 x 3 x 2 x 1 = 24 ways.
Example 3: In a school sports day, 5 students are running a race. You need to decide the order in which they finish. How many possible outcomes are there? Solution: There are 5! (5 factorial) ways to arrange them, which is 5 x 4 x 3 x 2 x 1 = 120 ways.
Common Mistakes to Avoid⚠️
- Mistake 1: Forgetting to multiply all the numbers in the factorial. For example, calculating 4! as 4 x 3 instead of 4 x 3 x 2 x 1.
- Mistake 2: Confusing the order of arrangement with combination, where order does not matter.
- Mistake 3: Not considering all possible arrangements, especially when conditions are given, such as 'A must be before B'.