0In the context of JEE Main, "combinations" refer to the mathematical concept of selecting items from a set where the order of selection doesn't matter. The key formula is nCr = n! / (r! * (n-r)!), where 'n' is the total number of items and 'r' is the number you're choosing. Understanding combinations is crucial for solving problems related to probability and arrangements in the JEE Main exam.
Here's a breakdown of key aspects of combinations for JEE Main:
1. Definition:
- A combination is a selection of items from a set where the order of selection is not important.
- For example, choosing 2 students out of a group of 5 for a committee is a combination problem.
2. Formula:
- The number of combinations of 'n' items taken 'r' at a time is denoted by nCr or C(n, r).
- The formula is: nCr = n! / (r! * (n-r)!).
- Where '!' denotes the factorial (e.g., 5! = 5 * 4 * 3 * 2 * 1).
3. Important Properties: nCr = nC(n-r), nCo = nCn = 1, nC1 = n, and nCr + nCr-1 = n+1Cr.
